resonant all-dielectric optical metamaterials · 2016-06-16 · working in a newly-started lab, ......
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Resonant All-Dielectric Optical Metamaterials
by
Yuanmu Yang
Dissertation
Submitted to the Faculty of the
Graduate School of Vanderbilt University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
in
Interdisciplinary Materials Science
August, 2015
Nashville, Tennessee
Approved:
Jason G. Valentine, Ph.D.
Richard F. Haglund Jr., Ph.D.
Deyu Li, Ph.D.
ii
To my beloved mom and dad.
iii
Acknowledgements
My journey towards the Ph.D. degree has probably been the most rewarding part
of my life, with the help from many people.
First and foremost, I would like to thank my adviser, Prof. Jason Valentine for his
unwavering support. Prof. Valentine offered me an opportunity to come to the United
States and join his lab fresh from undergrad. Since then, I was extremely fortunate to
work with the best, learned through him to be a critical thinker, nurtured by him to grow
to be a truly independent researcher. Working in a newly-started lab, I was lucky to have
Prof. Valentine guiding me hand by hand running experiments in the beginning days,
which developed not only my skill, but also the attitude as an experimentalist. During
these years at Vanderbilt, Prof. Valentine has always kept his door open to me for
discussion. He is always the best listener, and always offers the most insightful and
constructive suggestions for improvement, showing me the “big picture”. The sparklings
in the discussions eventually became the origins of many of the projects written in this
dissertation. Prof. Valentine is also extremely generous and supportive sending me to
numerous conferences and introducing me to his colleagues, which helped me interact
with the large optics community and built me the connections with future co-workers. His
mentorship and support is the single most important reason to my success in the last
several years, and he will always stand out as my role model in my future endeavor as a
researcher.
I would also like to thank Prof. Sharon Weiss, Prof. Richard Haglund, Prof. Deyu
Li and Prof. Yaqiong Xu for serving on my dissertation committee, for providing me
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opportunities for research rotations, and for valuable suggestions on my future career
options.
I want to especially thank all the Valentine group members, both past and present.
Their continuous help, discussion, and friendship have helped make my experience as a
graduate student not only productive but also fun. Despite of learning from each other, I
truly enjoyed all the happy hours and Bushwackers with these guys. Special thanks to
Parikshit Moitra for guiding me on everything ranging from nanofabrication to numerical
simulation. Special thanks to Wenyi Wang, who motivates me to go to the lab during
nights and weekends, and provides me all the faith and encouragement.
My dissertation research cannot be made possible without the help and support in
nanofabrication. Special thanks to Ivan Kravchenko, Daryl Briggs, Scott Retterer, Dale
Hensley, Kevin Lester, and Bernadeta Srijianto at CNMS, and Tony Hmelo, Bo Choi, and
Ben Schmidt at VINSE. The work in the cleanroom can be struggling, but your training
and assistance have made everything much easier.
Many of the friends made my life in Nashville so cheerful. Special thanks to Jialei
Song, who has been such an awesome roommate. Special thanks to Jing Wu, Doug
Waters and Jackie Waters, who helped me settle down in the first year when I had nothing
to embrace.
Special thanks to my undergraduate adviser Prof. Jiaguang Han, who introduced
me to the world of “metamaterial” when I barely knew anything about research, and
continued to guide me through later days.
Finally, I wish to express my deepest gratitude to my family for their
unconditional love, support and encouragement. It feels really good that I know you are
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always standing behind my back no matter what happens. To my mom, sending me off to
the United States for years is not easy. Thanks for letting me chase what I am passionate
about and what is best for my career. To my dad, sometimes I become impatient
explaining my research to you, but I wish that in the end, you feel proud seeing your son
going so far.
Financial support for my graduate studies was provided in part by grants from
the National Science Foundation, Office of Naval Research and the United States –Israel
Binational Science Foundation. Work performed at CNMS was sponsored at Oak Ridge
National Laboratory by the Scientific User Facilities Division, Office of Basic Energy
Sciences, US Department of Energy.
vi
Table of Contents
Acknowledgements .......................................................................................................... iii
List of Figures ................................................................................................................... ix
List of Abbreviations ..................................................................................................... xvi
List of Publications ...................................................................................................... xviii
Chapter 1 Introduction..................................................................................................... 1
1.1 What is an Optical Metamaterial? .................................................................................... 1 1.2 Engineering Optical Properties of Materials .................................................................... 2 1.3 Components of Conventional Metamaterials ................................................................... 4 1.4 Metamaterials beyond Engineered Refractive Index ...................................................... 9
1.4.1 Spatially-varying 2D Metasurfaces for Phase Control .............................................. 9 1.4.2 Metasurfaces with Designer Dispersion Profiles ..................................................... 11 1.4.3 Nonlinear Metamaterials ......................................................................................... 12
1.5 Plasmonic Metamaterial Challenges ............................................................................... 13 1.6 Resonant Dielectric Metamaterials ................................................................................. 14 1.7 Organization of the Thesis ................................................................................................ 18
Chapter 2 3D Dielectric Metamaterials — Zero Refractive Index ............................ 21
2.1 Introduction ....................................................................................................................... 21 2.2 Photonic Dirac Cone and Zero Index Design ................................................................. 23 2.3 Fabrication and Optical Characterization ...................................................................... 25 2.4 Directive Quantum Dot Emission .................................................................................... 32 2.5 Conclusion.......................................................................................................................... 34
Chapter 3 2D Dielectric Metasurface — Meta-Reflectarray ...................................... 36
3.1 Introduction ....................................................................................................................... 36 3.2 Broadband Linear Polarization Conversion................................................................... 38 3.3 Broadband Optical Vortex Generation ........................................................................... 43 3.4 Conclusions ........................................................................................................................ 49
Chapter 4 2D Dielectric Metasurface — Analogue of Electromagnetically Induced
Transparency................................................................................................................... 51
4.1 Introduction ....................................................................................................................... 51 4.2 Design and Characterization ............................................................................................ 53 4.3 Theoretical Treatment ...................................................................................................... 56 4.4 Refractive Index Sensing .................................................................................................. 62
vii
4.5 Conclusion.......................................................................................................................... 65
Chapter 5 2D Dielectric Metasurface — Enhanced Nonlinearity .............................. 66
5.1 Introduction ....................................................................................................................... 66 5.2 Linear Optical Properties ................................................................................................. 68 5.3 Enhanced Third Harmonic Generation and Nonlinear Kerr Effect ............................ 70 5.4 Absolute Third Harmonic Efficiency .............................................................................. 75 5.5 Conclusion.......................................................................................................................... 76
Chapter 6 Metamaterial Perfect Absorber-based Quantum Well Infrared
Photodetector................................................................................................................... 78
6.1 Introduction ....................................................................................................................... 78 6.2 Background ........................................................................................................................ 80
6.2.1 Intersubband Transitions & Quantum Well Infrared Photodetectors ...................... 80 6.2.2 Optical Coupling Method for Quantum Well Infrared Photodetectors ................... 82
6.3 Design of a Metamaterial Perfect Absorber with Integrated Quantum Wells ............ 84 6.3.1 One-dimensional Polarization-sensitive Design ...................................................... 84 6.3.2 Device Performance Versus Incident Angle ............................................................ 87 6.3.3 Two-dimensional Polarization-Insensitive Design .................................................. 89 6.3.4 Routes Towards Device Fabrication and Characterization ...................................... 89
6.4 Conclusion.......................................................................................................................... 90
Chapter 7 Conclusion and Outlook ............................................................................... 92
7.1 Conclusion.......................................................................................................................... 92 7.2 Future Outlook of Metamaterials .................................................................................... 94
Appendix A: Zero-index Metamaterial ........................................................................ 96
A.1 Retrieval of the effective index from the Bloch modes .................................................. 96 A.2 Optical property retrieval from the Bloch modes and extended states ....................... 96 A.3 Optical property retrieval from the Bloch modes and extended states ....................... 97
Appendix B: Meta-reflectarray ................................................................................... 100
B.1 Fabrication of Meta-reflectarray .................................................................................. 100 B.2 Device Performance with Changing Incident Angle ................................................... 101
Appendix C: Dielectric Metasurface Analogue of Electromagnetically Induced
Transparency................................................................................................................. 103
C.1 Q-factor Extraction ........................................................................................................ 103
Appendix D: Nonlinear Dielectric Fano-resonant Metasurface ............................... 105
D.1 Measurement Set-up ...................................................................................................... 105 D.1.1 Linear/Nonlinear Spectroscopy ............................................................................. 105 D.1.2 Absolute THG Efficiency-Measurement from OPO ............................................. 106 D.1.3 Absolute THG Efficiency-Measurement from OPA ............................................. 107
viii
D.2 Device Performance versus Incident Angle ................................................................. 108
Bibliography .................................................................................................................. 110
ix
List of Figures
Figure 1.1. Available optical properties of materials characterized by the electric
permittivity ( ) and magnetic permeability ( ). .............................................................. 4
Figure 1.2. (a) Metal wire structure exhibiting negative ε [12]. (b) Split-ring resonator
(SRR) structure exhibiting negative μ , introduced by Pendry et al. The inset shows the
equivalent circuit model for the SRR[13]. (c) First experimental negative index structures,
constituted of metal wires and SRRs, introduced by Smith et al[14]. (d) Experimental set-
up for the measurement of left-handedness of the metamaterial structure shown in panel
(c) at 5 GHz [1]. .................................................................................................................. 6
Figure 1.3. Development of metal-based metamaterial as a function of operation
frequency and time. Orange: double SRRs[14]; green: U-shaped SRRs[16]; blue: metallic
cut-wire pairs[17]; red: double fishnet structures[3]. The four insets show optical or
electron micrographs of the five kinds of structure. Figure adapted from ref. [18]. .......... 8
Figure 1.4. (a) Left: scanning electron microscopy image of a metasurface that generates
a linear phase gradient via an array of V-shaped gold meta-atoms. The phase gradient
mimics the effects of a blazed phase grating. Right: measured far-field intensity
profiles[23]. (b) Left: schematic showing a metasurface quarter-wave plate. The unit cell
consists of two subunits (pink and green) offset by d = Γ/4[24]. (c) Schematic
demonstrating how a phase-graded metasurface can generate holograms. Each meta-atom
acts as a phase modifying pixel that, on illumination with circularly polarized light,
generates the required local phase profile for holographic reconstruction in the
transmitted beam of opposite helicity[25]. (d) Left: on propagation through an
appropriate metasurface, the rapid phase retardation generates a strong spin–orbit
interaction leading to an accumulation of circularly polarized components in the
transverse directions of the beam. Right: observation of the PSHE via measurement of the
helicity of the anomalously refracted beam from a linearly phase-graded metasurface
formed from V-shaped elements[26]. Figure adapted from ref. [27]. .............................. 10
Figure 1.5. (a) Upper panel: calculated dipole amplitudes of the bonding and antibonding
collective dipolar plasmon modes in a gold nanoshell heptamer. Measured (Middle panel)
and calculated (Lower panel) scattering spectra of a gold nanoshell heptamer[28]. (b)
Upper panel: scanning electron microscope image of the stacked plasmonic EIT analogue
structure. The red color represents the gold bar in the top layer and the green color
represents the gold wire pair in the bottom layer. Inset: enlarged view. Lower panel:
experimental transmittance spectrum of the sample. The fitting curve was calculated from
a Fano-type EIT model simulation[29]. Figure adapted from ref. [30]. ........................... 11
Figure 1.6. (a) Second harmonic generation from an array of SRRs exhibiting magnetic
resonances[31]. (b) Third harmonic generation from a plasmonic bowtie antenna coupled
to an ITO nano-crystal[32]. (c) Schematic demonstrating all-optical modulation from a
x
plasmonic metasurface[33]. (d) Schematic showing phase mismatch-free four wave
mixing[34]......................................................................................................................... 13
Figure 1.7. Illustration of Mie resonances in dielectric cubes. The curve shows the
scattering cross-section (SCS) of a Si nano-cube with a length of 500 nm. The two peaks
in the SCS plot correspond to a magnetic and electric dipole resonance, respectively. ... 15
Figure 1.8. Schematic showing an array of dielectric spheres with permittivity 2
embedded in a host medium with permittivity 1 [39]. ...................................................... 16
Figure 1.9. (a) Schematic of a silicon nano-rectangle antenna with length Lx, width Ly
and height Lz. (b) The scattering cross-sections of the silicon nano-antenna as a function
of the antenna length Lx. The solid lines represent electric dipole resonance, and the
dashed line represent the magnetic dipole resonance. ...................................................... 17
Figure 2.1. Schematic of light propagation in the air and ZIM, respectively. ................. 21
Figure 2.2. (a) Diagram of the ZIM structure with a unit cell period of a = 600 nm and w
= t = 260 nm. (b) Band diagram of uniform bulk ZIM (infinitely thick) for TM
polarization. Dirac cone dispersion is observed at the Γ point with triple degeneracy at
211 THz. The shaded area denotes regions outside the free-space light line. (c) Retrieved
effective permittivity and permeability of the bulk ZIM acquired using field-averaging.
The inset shows the electric and magnetic fields within a single unit cell at the zero-index
frequency indicating a strong electric monopole and magnetic dipole response. (d) IFC of
the TM4 band. The contours are nearly circular (i.e., isotropic) for a broad frequency
range and increase in size away from the zero-index frequency indicating a progressively
larger refractive index. ...................................................................................................... 25
Figure 2.3. (a)-(d) Schematic of the detailed fabrication steps. (e)-(f) SEM image of the
fabricated sample (e) before and (f) after PMMA filling. ................................................ 26
Figure 2.4. Experimental (red) and theoretical transmittance (dotted blue) curves of the
ZIM (200 x 200 µm2 total pattern area). Regions corresponding positive index, metallic
properties, and negative index are denoted with blue, grey, and yellow shading,
respectively. ...................................................................................................................... 29
Figure 2.5. (a) Effective permittivity and permeability of the fabricated ZIM obtained
using S-parameter retrieval. Regions corresponding positive index, metallic properties,
and negative index are denoted with blue, grey, and yellow shading, respectively. (b)
Effective refractive index of the fabricated structured obtained using S-parameter
retrieval. ............................................................................................................................ 30
Figure 2.6. (a) IFCs of air and a low-index metamaterial illustrating angularly selective
transmission due to conservation of the wave vector parallel to the surface. (b) Simulated
angle and wavelength-dependent transmittance of the fabricated structure. (c)-(f) Fourier-
plane images of a beam passing through the fabricated ZIM structure within the low
xi
index band. Angularly selective transmission can be observed in the y-direction due to the
low effective index. Along the x-direction, angular selectivity is not preserved due to the
one-dimensional nature of Si rods. (g) Fourier-plane image of the illumination beam
demonstrating uniform intensity over the angular range measured. ................................. 32
Figure 2.7. (a) Schematic of laser-pumped QD emission from within the ZIM structure.
(b) Photoluminescence (PL) spectrum of PbS quantum dots (Evident Technology) used in
the main text. The emission peak appears at 1425 nm, with a full-width at half-maximum
of 172 nm. The blue-, gray- and yellow-shaded region corresponds to positive index,
metallic properties, and negative index as acquired from S-parameter retrieval. The dip of
measured luminescence spectrum at around 1380 nm is due to the water absorption line.
(c) 2D Fourier-plane images of quantum dot emission on the substrate, intensity is scaled
by two times. (d) 2D Fourier-plane images of QD emission within the ZIM. ................. 34
Figure 3.1. (a) Schematic of the meta-reflectarray with a unit cell period of p = 650 nm, a
= 250 nm, b= 500 nm, t1 = 380 nm and t2 = 200 nm. In the fabricated sample the
resonators are embedded in PMMA and a quartz wafer caps the resonators. (b) SEM
image of the sample before spin-coating PMMA and depositing the silver film. ............ 39
Figure 3.2. (a) Schematic of the polarization conversion measurement set-up. (b)
Measured and simulated reflectance for co- and cross-polarized light. (c) Polarization
conversion efficiency of the device. The shaded regions indicate the wavelength range
where experimental measurements were not possible due to low detector quantum
efficiency (d) Schematic of the decomposition of linearly polarized incident and reflected
light. (e)-f) Reflectance and phase for x and y polarized light demonstrating near-unity
reflection and a broadband π phase shift........................................................................... 40
Figure 3.3. (a) Schematic of the multiple reflections. (b) Comparison between the
calculated reflected field from multiple reflections and the simulated overall reflected
field. .................................................................................................................................. 42
Figure 3.4. Simulated cross-polarized reflection (a) magnitude and (b) phase for
resonators with varying geometry at a fixed wavelength of 1550 nm. The unit cell period
is set as 650 nm and the PMMA spacer thickness is set to 150 nm. (c) Schematic of eight
resonators that provide a phase shift from 0 to 2π. The dimension of resonators 1-4 are 1)
a=200nm, b=425nm; 2) a=225nm, b=435nm; 3) a=250nm, b=450nm; 4) a=275nm,
b=475nm. Resonators 5-8 are simply rotated by 90° with respect to resonators 1-4.
Simulated cross-polarized reflection (d) amplitude and (e) phase for arrays of resonators
1-8 as a function of the incident wavelength. The phase delay of array 1 is set to 0 for
each wavelength to serve as a reference. .......................................................................... 45
Figure 3.5. (a) Optical microscope image of the fabricated spiral phase plate composed
of eight sections of Si cut-wires, providing an incremental phase shift of π/4. (b) SEM
image showing the cut-wires at the center of the reflectarray. (c-e) Experimentally
measured intensity profiles of the generated vortex beam with topological charge l=1.
The wavelengths of incident light are (c) 1500 nm, (d) 1550 nm, and (e) 1570 nm. (f-h)
Interference pattern of the vortex beam and the co-propagating Gaussian beam when the
xii
beam axes are tilted with respect to one another. (i-k) Interference pattern of a vortex
beam and a Gaussian beam which have collinear propagation. In (c-k) a linear polarizer is
placed in front of the camera to filter out co-polarized light. (l-m) Interference pattern of
the vortex beam and the Gaussian beam in the absence of the linear polarizer. ............... 47
Figure 3.6. (a) Electric field plot of the meta-reflectarray illumined with a normally
incident x-polarized Gaussian beam with a wavelength of 1550 nm and waist of 7µm.
The metasurface is composed of the 8 Si cut-wire resonators from Fig. 3 with a unit cell
period of 650 nm. (b) Far-field scattered light as a function of angle for both co- and
cross-polarizations. The dotted line corresponds to the solution of the generalize Snell’s
law and matches well with the full-wave simulation. ....................................................... 49
Figure 4.1. (a) Diagram of the metasurface. The geometrical parameters are: = 150 nm,
= 720 nm, = 110 nm, = 225 nm, = 70 nm, = 80 nm, = 110nm, = 750 nm and = 750
nm. (b) Schematic of interference between the bright and dark mode resonators. (c)
Simulated transmittance (blue curve), reflectance (red curve), and absorption (green
curve) spectra of the metasurface. (d) Oblique scanning electron microscope image of the
fabricated metasurface. (e) Enlarged image of a single unit cell. (f) Experimentally
measured transmittance, reflectance, and absorption spectra of the metasurface. ........... 54
Figure 4.2. (a) Schematic showing the coupling of the bright mode resonator to the
neighboring dark mode resonator. Here, we schematically provide the fields arising due
to the bright mode resonance. (b) Simulated magnetic and electric field amplitudes as a
function of resonator spacing. (c) Transmittance curve for the metasurface with varying
values of 1g obtained through FEFD simulation. 2 1g g is used to track the difference
in spacing between the bright mode resonator and the adjacent dark mode resonators. (d)
The extracted Q-factors of the EIT resonance as a function of . ................................... 58
Figure 4.3. (a) Vector plot of the magnetic field showing the coherent excitation of the
magnetic dipoles within the dark mode resonators. (b) Scanning electron microscope
images of the dielectric metasurface with different array sizes. The inset shows the
magnified view of a 20 by 20 array. (c) Transmittance spectra of arrays with different
sizes. d, The extracted Q-factors of the metasurface as a function of array size. ............. 59
Figure 4.4. (a) Diagram of the metasurface. The geometrical parameters are: 2a = 150 nm,
2b = 600 nm, 2inr = 120 nm, 2outr = 250 nm, 3g
= 70 nm, 4g = 50 nm, = 110nm, 3p =
750 nm and 4p = 800 nm. (b) Simulated electric field amplitude distribution. (c)
Scanning electron microscope image of the fabricated metasurface. The inset shows a
single unit cell (scale bar of 200 nm). (d) Simulated (blue solid line) and measured (red
dashed line) transmittance spectrum of the metasurface. ................................................. 62
Figure 4.5. (a) SEM image of the sample with the quartz substrate etched by 100 nm. (b)
Measured transmittance spectra of the EIT metasurface when immersed in oil with
refractive index ranging from 1.40 to 1.44. (c) The red circles show the experimentally
measured resonance peak position as a function of the background refractive index. The
t
xiii
blue curve is a linear fit to the measured data, which was used to determine the sensitivity
as 289 nm RIU-1
. ............................................................................................................... 63
Figure 4.6. (a) SEM image of the double-gap split-ring sample with the quartz substrate
etched by 100 nm. The inset is an enlarged image of a single unit cell (scale bar of 200
nm). (b) Measured transmittance spectra of the double-gap split-ring metasurface when
immersed in oil with refractive index ranging from 1.40 to 1.44. (c) The red circles show
the experimentally measured resonance peak position as a function of the background
refractive index. The blue curve is a linear fit to the measured data, which was used to
determine sensitivity of the structure as 379 nm/RIU. ..................................................... 65
Figure 5.1. (a) Schematic of three photon up-conversion with the Fano-resonant silicon
metasurface. The blue bar resonators represent the “bright” mode, and the red disk
resonators represent the “dark” mode. (b) Diagram of one unit cell of the metasurface.
The geometrical parameters are: a = 200 nm, b = 700 nm, r = 210 nm, g = 60 nm, =
120nm, 1p
= 750 nm and2p = 750 nm. (c) Schematic of the Fano interference between
the bright and dark mode resonators. (d) An SEM image of the fabricated metasurface. (e)
Simulated (blue) and experimentally measured (red) transmittance spectra of the
metasurface. ...................................................................................................................... 70
Figure 5.2. (a) Simulated electric field amplitude at the Fano resonance peak wavelength
of 1350 nm in both the x-y and y-z plane. The choice of cut-plane is represented with the
white dashed lines. (b) Third harmonic spectra of the metasurface with the incident
electric field polarized along x-axis and y-axis, respectively. (c) Third harmonic spectra
of an un-patterned Si film and a bare quartz substrate, respectively (average pump power
of 25 mW, peak pump intensity of 1.6 GW cm-2
). ........................................................... 72
Figure 5.3. (a) The wavelength-dependent THG intensity of the metasurface when
normalized to an un-patterned Si film of the same thickness. The blue points are data
taken under 0.8 GW cm-2
peak pump intensity, and the red points are data taken under 1.6
GW cm-2
peak pump intensity. The black dash line indicates the linear Fano resonance
peak. (b) Simulated transmittance of the metasurface under different pump intensity. The
measured transmittance under low power white light illumination is also shown as the
black dashed line for a reference. (c) The relative change in transmittance as a function of
pump power at 1348 nm, 1352 nm and 1356 nm. The black dash line shows the shift of
the transmittance peak with increasing pump power. ....................................................... 74
Figure 5.4. (a) Log-log plot of the third harmonic power as a function of the pump power
and the peak pump intensity with OPO. The red circles indicate the measured data, and
the blue line is a numerical fit to the data with a third-order power function. The green
circle denotes the pump power at which the photograph in panel b was taken. The inset
shows the extracted absolute THG efficiency as a function of the pump power. (b) A
photograph taken under ambient room light showing blue light emission from the sample
for an incident wavelength at 1350 nm (average pump power of 50 mW, peak pump
intensity of 3.2 GW cm-2
). (c) Log-log plot of the third harmonic power as a function of
t
xiv
the pump power and the peak pump intensity with OPA. The inset shows the extracted
absolute THG efficiency as a function of the pump power. ............................................. 76
Figure 6.1. (a) An SEM image of a thermally controlled reconfigurable photonic
metamaterial[166]. (b) Experimental design of an active THz metamaterial device based
on carrier injection into the GaAs substrate[167]. (c) Hybrid split-ring resonator
metamaterials based on vanadium dioxide[168]. (d) Schematic rendering of a gate-
controlled active graphene metamaterial composed of a SLG deposited on a layer of
hexagonal metallic meta-atoms[169]. ............................................................................... 80
Figure 6.2. (a) Band diagram of interband transition occurring in a conventional intrinsic
infrared photodetector. (b) Band structure of a QW. Intersubband transition between
electron levels E1 and E2 is schematically shown. ............................................................ 82
Figure 6.3. (a) Conventional 45 degree wedge waveguide coupling. (b) Schematic
diagram of 2-D periodic gratings. (c) Layer diagram of a four-band QWIP device and the
deep groove periodic grating structure. Figure adapted from ref.[174]. ........................... 83
Figure 6.4. 3D view of the quantum well-integrated metamaterial perfect absorber. The
top and bottom Au layers have a thickness of 50 nm. The other geometric parameters are
p=3500 nm, a=1500 nm, t=1000 nm. ............................................................................... 84
Figure 6.5. The real and imaginary permittivity of the GaAs quantum well along the z-
(quantum well growth)-direction. ..................................................................................... 85
Figure 6.6. Transmission, reflection and absorption spectra of the structure from full
wave simulation under normal plane wave illumination. ................................................. 86
Figure 6.7. (a) Vector plot of the electric field from full wave simulation with the
frequency of incident light at 30 THz. (b) Simulated magnetic and electric field
amplitudes with the frequency of incident light at 30 THz. ............................................. 87
Figure 6.8. The simulated angular dispersions of the absorbance peak for TE(a) and TM
configurations(b). .............................................................................................................. 88
Figure 6.9. (a) 3D view of the quantum well-integrated metamaterial perfect absorber.
The top and bottom Au layers have a thickness of 50 nm. The other geometric parameters
are p=3500 nm, a=1500 nm, t=1800 nm, w=400 nm. (b) Simulated absorption spectra of
the structure under normal plane wave illumination with electric field polarized along x-
direction (blue) and y-direction (red), respectively. .......................................................... 89
Figure A.1. (a) The solid lines represent the band structure of the square lattice
calculated from MPB and the circles correspond to band diagram retrieved from effective
index and the dispersion relation . The mismatch of the two methods
at the band edge is due to the fact that the effective medium approximation no longer
holds in those regions. (b) Extended states of the crystal showing that only one band
xv
(TM4) is present between 215 THz and 225 THz, allowing an effective index to be
assigned to this region. ...................................................................................................... 97
Figure A.2. (a)-(c), Light incidence at 0°, 10°, 30° respectively at wavelength of 1340
nm. (d)-(f), Light incidence at 0°, 5°, 20° respectively at wavelength of 1380 nm. (g)-(i),
Light incidence at 0°, 5°, 20° respectively at wavelength of 1458 nm. ............................ 99
Figure B.1. (a) LPCVD silicon on quartz. (b) EBL patterning. (c) Etch mask deposition
and lift-off. (d) RIE. (e) PMMA spinning and silver deposition. ................................... 101
Figure B.2. Cross-polarization reflectance as a function of incident angles for (a) s- and
(b) p-polarized light respectively. ................................................................................... 102
Figure C.1. Fano fit of the experimentally measured transmittance spectrum. ............. 104
Figure D.1. Schematic of the linear/nonlinear spectroscopic measurement set-up for the
investigation of the metasurface. .................................................................................... 106
Figure D.2. Schematic of the absolute THG efficiency measurement set-up with OPO.
......................................................................................................................................... 107
Figure D.3. Schematic of the absolute THG efficiency measurement set-up with OPA.
......................................................................................................................................... 108
Figure D.4. Simulated Linear transmittance of the metasurface as a function of incident
angle for (a) s- and (b) p-polarized light. ........................................................................ 109
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List of Abbreviations
CCD Charge-coupled Device
CNMS Center for Nanophase Material Sciences
EBL Electron Beam Lithography
EIT Electromagnetically Induced Transparency
ENZ Epsilon Near Zero
FDTD Finite Difference Time Domain
FEFD Finite Element Frequency Domain
FOM Figure of Merit
FTIR Fourier Transform Infrared Spectroscopy
FWHM Full Width at Half Maximum
HCG High Contrast Grating
IFC Iso-frequency Contour
LPCVD Low Pressure Chemical Vapor Deposition
MBE Molecular Beam Epitaxy
MEMS Microelectromechanical
MOCVD Metal-Organic Chemical Vapor Deposition
OPA Optical Parametric Amplifier
OPO Optical Parametric Oscillator
PCR Polarization Conversion Rate
PDMS Poly(dimethylsiloxane)
PMMA Poly(methyl methacrylate)
xvii
PMT Photo Multiplier Tube
QD Quantum Dot
Q-factor Quality Factor
QW Quantum Well
QWIP Quantum Well Infrared Photodetector
RIE Reactive-ion Etch
RIU Refractive Index Unit
SEM Scanning Electron Microscopy
SCS Scattering Cross-Section
SNR Signal to Noise Ratio
SRR Split-ring Resonator
TE Transverse Electric
THG Third Harmonic Generation
TM Transverse Magnetic
TPA Two Photon Absorption
VINSE Vanderbilt Institute of Nanoscale Science
and Engineering
ZIM Zero Index Metamaterial
xviii
List of Publications
Portion of this dissertation have been drawn from the following publications and
manuscripts:
1. Y. Yang, Abdelaziz Boulesbaa, I. Kravchenko, D. Briggs, Alexander Pretzky, David
Geohegan and J. Valentine, “Nonlinear Fano-resonant Dielectric Metasurface”,
submitted to Nature Communications.
2. Y. Yang, I. Kravchenko, D. Briggs and J. Valentine, “All-dielectric metasurface
analogue of electromagnetically induced transparency”, Nature Communications, 5,
5753 (2014)
3. Y. Yang, W. Wang, P. Moitra, I. Kravchenko, D. Briggs and J. Valentine, “Dielectric
meta-reflectarray for broadband polarization conversion and optical vortex
generation”, Nano Letters 14, 1394 (2014)
4. P. Moitra†, Y. Yang
†, Z. Anderson, I. Kravchenko, D. Briggs and J. Valentine,
“Realization of an all-dielectric zero-index optical metamaterial”, Nature Photonics 7,
791 (2013) (†: equal contribution)
1
Chapter 1 Introduction
1.1 What is an Optical Metamaterial?
Engineering material properties at will has long been a dream for scientists.
However, natural materials are composed of individual atoms tightly arranged with
separation on the order of angstroms; therefore, tailoring material properties through
designing and synthesizing materials composed of “artificial” atoms can be an extremely
challenging task due to the current technological constraints.
However, the task to engineer, specifically, the optical properties of materials at
will can be much easier to accomplish through metamaterials. An optical metamaterial is
a composite formed from so-called “meta-atoms”. In order to have the composite of
“meta-atoms” be treated as a homogeneous effective material for light, the unit cell size
needs to be smaller than the wavelength of light (typically on the order of microns), while
it can be much larger than that of the real atoms. Fortunately, the advances in
nanotechnology have now enabled us to create the optical version of “meta-atoms”
through either top-down or bottom-up fabrication techniques.
Metamaterials free us from the constraints of naturally occurring materials and
allow for full control over light flow through the design of artificial “meta-atoms”.
Careful design of each unit cell can enable a wide variety of new material properties.
During the rapid development of metamaterial research in the last decade, many
previously science-fiction-like material properties and devices have been realized,
including but not limited to negative refractive index[1]–[3], sub-diffraction-limit
superlenses[4]–[6] and invisibility cloaks[7]–[10].
2
1.2 Engineering Optical Properties of Materials
The most common way that we can define and understand the optical properties
of an material is based on their constitutive properties: electric permittivity, , and
magnetic permeability, . These properties describe how the material interacts with light.
Permittivity is a measure of how the applied electric field interacts with the medium and
permeability measures the response of a material to an applied magnetic field. To develop
a better understanding of this, we can derive the wave equation for light propagation
through a homogeneous medium from the Maxwell’s equations,
0,
,
,
,
t
t
Β
BΕ
D
DH j
(1.1)
where E is the electric field, H is the magnetic field, B is the magnetic flux density, D is the
electric flux density, is the charge density, and j is the current density.
Combining equations (1.1) with the constitutive relations,
0
0
r
r
D E E
B H H (1.2)
we can arrive at the wave equations,
22
2
22
2
t
t
EE
BB
(1.3)
where 12
0 8.85 10 F/m is the permittivity of vacuum, and 6
0 1.26 10 H/m is the
vacuum permeability; r and r are the relative permittivity and permeability,
respectively; and the refractive index of an material is then defined as r rn . The
3
wave equations govern how electromagnetic wave interacts with matter, and can be
applied to form the complete description of light transmission, reflection, refraction,
scattering and absorption. In Fig. 1.1, we group materials based on the sign of their ε and
. The signs of these properties determine many of the unusual responses that can be
engineered. Most natural materials have positive ε and and thus fall into quadrant I of
this graph. Materials with negative ε but positive fall into quadrant II and include
metals, heavily doped semiconductors, or ferroelectric materials that can have negative
values of below the plasma frequency. The third quadrant is where we find negative
index materials, with both negative ε and negative . The last quadrant of this material
landscape is where is positive, but is negative. There are also very few natural
materials in this regime, although some ferrite materials exhibit these properties at
microwave frequencies. It should also be noted that there is a special region lying in the
center of the graph, where and both approach zero. At such a region, the refractive
index of the material approaches zero, while the impedance of the material Z
can be matched to the free space.
Much of the exciting research in metamaterials and plasmonics is tied to the fact
that we can engineer both the electric and magnetic “arms” of light, ignoring the
constraints on and imposed by naturally occurring materials.
4
Figure 1.1. Available optical properties of materials characterized by the electric
permittivity ( ) and magnetic permeability ( ).
1.3 Components of Conventional Metamaterials
The original idea of a negative index material, one of the most commonly
mentioned metamaterials, was first outlined by Veselago in 1968[11]. This type of
material has been referred to conceptually as a left-handed material as one of the effects
of negative is a reversal of the direction of propagation of the incident wave, thus
breaking the right-hand rule of elementary physics. However, the first experimental
realization of an actual left-handed material arrived almost 30 years after the original
proposal [13].
To construct a metamaterial with a negative, or any other arbitrary refractive
index, it is necessary to engineer the response of the material to both the electric and
magnetic “arm” of the impinging light. To create a material with negative electric
n
5
permittivity is in fact quite straightforward. Many naturally occurring materials such as
metal and highly-doped semiconductors possess a negative permittivity at frequencies
below their plasma frequency. With unbound quasi-free electrons the dielectric function
can be described using the Drude model,
2
1p
i
(1.4)
where2
0p e en e m is the plasma frequency of the metal or semiconductor, and is the
damping coefficient. However, using only naturally occurring materials it is difficult to
acquire the artificial permittivity at the desired operating frequency since the electron
density and therefore the plasma frequency of metal can hardly be modified.
6
Figure 1.2. (a) Metal wire structure exhibiting negative ε [12]. (b) Split-ring resonator
(SRR) structure exhibiting negative μ , introduced by Pendry et al. The inset shows the
equivalent circuit model for the SRR[13]. (c) First experimental negative index structures,
constituted of metal wires and SRRs, introduced by Smith et al[14]. (d) Experimental set-
up for the measurement of left-handedness of the metamaterial structure shown in panel
(c) at 5 GHz [1].
To achieve a designer permittivity, the effective medium approach can be taken.
In other words, one can manufacture a “diluted metal” by embedding the metal in a
dielectric background medium. For example, metallic wires with a permittivity m can be
embedded in a host dielectric medium of permittivity i , as is schematically shown in Fig.
1.2(a). According to the effective medium theory, for a metallic wire grid, the effective
permittivity of the composite material along the wire axis can be described simply as,
7
1eff m if f (1.5)
where f is the filling fraction of the metal. Therefore, by simply tuning the filling
fraction of the metal, one can achieve a large tunability of the permittivity of the
composite material.
Creating a material with negative magnetic permeability can be much more
complicated, as in the optical frequencies there is no magnetic response ( 1 ) in
naturally-occurring materials. In fact, the creation of artificial magnetism was the biggest
impediment of the realization of negative refractive index after Veselago’s theoretical
proposal. In 1999, Sir John Pendry proposed one approach to realize the high frequency
magnetism using the so-called “split-ring resonator (SRR)”[15], as is shown in Fig.
1.2(b). The response of the SRR can be described using equivalent circuit theory where
the SRR is treated as a LC circuit with a natural resonant frequency of 0 1 LC ,
where L is the effective inductance and C is the effective capacitance of the structure.
When the frequency of the incident wave equals the resonant frequency 0 , the incident
wave can drive a circulating current through the resonator, inducing a strong magnetic
dipole moment, leading to the following expression foreff ,
2
2 2
0
1eff
F
i
(1.6)
where F is the area filling fraction of the SRR, and is the damping term.
8
Figure 1.3. Development of magnetic metamaterials as a function of operation frequency
and time. Orange: double SRRs[14]; green: U-shaped SRRs[16]; blue: metallic cut-wire
pairs[17]; red: double fishnet structures[3]. The four insets show optical or electron
micrographs of the five kinds of structure. Figure adapted from ref. [18].
Through proper engineering, negative permittivity and permeability can be
overlapped at the same operating frequency, leading to an effective negative refractive
index. In 2000, Smith, for the first time, experimentally demonstrated a material
possessing negative refractive index at microwave frequency by combining metallic
wires and SRRs[14]. The device photograph and a prism-based measurement set-up is
shown in Fig. 1.2(c)-(d). Following that, there has been a constant drive to shrink down
the unit cell size of the metamaterial and therefore to move its operating band to terahertz
and higher frequencies. To date, negative or zero index metamaterials up to visible
frequencies have been reported, as is summarized in Fig. 1.3. However, there are still
significant issues associated with the current-generation of optical metamaterial devices.
One particular problem is the large ohmic loss from metals at high frequencies.
9
Overcoming this problem will be one focus of this thesis and will be discussed in detail
later.
1.4 Metamaterials beyond Engineered Refractive Index
Although metamaterial research was initially focused on the possibility of
realizing negative refractive index, the scope of research has gone far beyond this point.
For example, transformation optics has opened a new avenue for us to route light around
an object, leading to an effective invisibility cloak[8]–[10], [19], [20]; chiral
metamaterials have enabled us to manipulate different polarization states of light[21],
[22]. Here I elaborate a few research directions most relevant to this thesis:
1.4.1 Spatially-varying 2D Metasurfaces for Phase Control
After more than a decade of research into metamaterials a low-cost and easy-to-
implement technique for fabricating three-dimensional (3D) optical metamaterials still
has not been found, though moderate improvement have been made. Techniques such as
two-photon lithography, projection membrane lithography, and molecular self-assembly
suffer from low speed, high complexity, and low tunability. Gradually, researchers have
begun to realize that ultrathin 2D meta-surfaces with designer properties can also be
extremely versatile in controlling light-matter interactions but with a much easier
fabrication requirement.
For example, conventional optical components such as lenses and waveplates
shape the wavefront of light by relying on the gradual phase accumulation along
distances much greater than the wavelength of light. However, recent developments in
10
ultrathin metasurfaces show that the dependence on propagation can be broken by
introducing an abrupt change of optical properties at an interface. The metasurface is
made of arrays of scatters such that control over the optical properties can be achieved by
engineering the interaction between light and the scatterers. A spatially-varying array of
antennas can be used to mold the intensity and/orphase, and therefore optical wavefronts
can be designed at will. Fig. 1.4 lists several of examples showing how 2D plasmonic
metasurfaces can be applied to realize anomalous refraction, polarization conversion,
holograms, and enhanced the photonic spin-hall effect[23]- [22].
Figure 1.4. (a) Left: scanning electron microscopy image of a metasurface that generates
a linear phase gradient via an array of V-shaped gold meta-atoms. The phase gradient
mimics the effects of a blazed phase grating. Right: measured far-field intensity
profiles[23]. (b) Left: schematic showing a metasurface quarter-wave plate. The unit cell
consists of two subunits (pink and green) offset by d = Γ/4[24]. (c) Schematic
demonstrating how a phase-graded metasurface can generate holograms. Each meta-atom
acts as a phase modifying pixel that, on illumination with circularly polarized light,
generates the required local phase profile for holographic reconstruction in the
transmitted beam of opposite helicity[25]. (d) Left: on propagation through an
appropriate metasurface, the rapid phase retardation generates a strong spin–orbit
interaction leading to an accumulation of circularly polarized components in the
transverse directions of the beam. Right: observation of the PSHE via measurement of the
helicity of the anomalously refracted beam from a linearly phase-graded metasurface
formed from V-shaped elements[26]. Figure adapted from ref. [27].
11
1.4.2 Metasurfaces with Designer Dispersion Profiles
Figure 1.5. (a) Upper panel: calculated dipole amplitudes of the bonding and antibonding
collective dipolar plasmon modes in a gold nanoshell heptamer. Measured (Middle panel)
and calculated (Lower panel) scattering spectra of a gold nanoshell heptamer[28]. (b)
Upper panel: scanning electron microscope image of the stacked plasmonic EIT analogue
structure. The red color represents the gold bar in the top layer and the green color
represents the gold wire pair in the bottom layer. Inset: enlarged view. Lower panel:
experimental transmittance spectrum of the sample. The fitting curve was calculated from
a Fano-type EIT model simulation[29]. Figure adapted from ref. [30].
Another major direction in metasurface research is to create planar structures with
spectrally sharp, high-quality (-Q) resonances. The creation of the high-Q resonance
12
(typically deemed as Fano resonance) relies on the destructive interference of a “bright”
and a “dark” mode resonator. If these two resonators are brought in close proximity in
both the spatial and frequency domains, they can couple. This coupling leads to a
resonance in the system, resulting from the interference between the two pathways. Due
to the greatly reduced radiative loss of the excited dark resonant mode, the Fano
resonance can be extremely sharp, resulting in complete transmission, analogous to
electromagnetically induced transparency (EIT) from the sample across a very narrow
bandwidth. Such resonances can be utilized to realize modulators with large modulation
depth when active components such as “phase-change” materials or graphene are placed
in close in vicinity. In addition, such a high-Q metasurface is well suited for ultra-
sensitive detection of substances attached to it. For instance, an atomically-thin graphene
layer can induce a multifold change in the transmission of a metasurface.
1.4.3 Nonlinear Metamaterials
Previous studies of metamaterials typically focus on the linear properties of the
medium upon low intensity irradiation. However, with high intensity laser illumination,
the responses of metamaterials may not necessarily scale linearly. The nonlinear optical
response of a material can be described by,
1 2 32 3
0 0 ... D E E E E (1.7)
where n is the n-th order nonlinear susceptibility.
Nonlinearity is the key for a variety of interesting and useful effects such as
parametric frequency up-/down- conversion, power amplification, and power-dependent
light transmission. Due to the great flexibility in terms of tuning the optical near-field and
13
therefore the effective nonlinear susceptibility, metamaterials have been proposed to
greatly boost the efficiency of harmonic generation[32] for phase mismatch-free four
wave mixing and even all-optical light modulation[34].
Figure 1.6. (a) Second harmonic generation from an array of SRRs exhibiting magnetic
resonances[31]. (b) Third harmonic generation from a plasmonic bowtie antenna coupled
to an ITO nano-crystal[32]. (c) Schematic demonstrating all-optical modulation from a
plasmonic metasurface[33]. (d) Schematic showing phase mismatch-free four wave
mixing[34].
1.5 Plasmonic Metamaterial Challenges
To date, most proposed metamaterial designs are based on subwavelength
metallic (plasmonic) resonators. For example, the first experimental realization of a
negative index metamaterial was based on the use of copper split-ring resonators at
14
microwave frequencies[35]. Other variations such as plasmonic fishnet structures have
also been proposed to simplify the realization and reduce loss at optical frequencies[9],
[36]. However, plasmonic metamaterials suffer from several key problems. First, metal
suffers from conduction loss at high frequencies, and such loss can be greatly amplified
when resonances are present. Although loss compensation methods such as incorporating
gain materials have been proposed, they tend to greatly complicate the device layout[37].
Secondly, metallic resonators normally do not possess an isotropic optical response.
Several authors have suggested methods to construct isotropic metamaterials by
combining metallic SRRs and wires. However it is difficult to fabricate bulk arrays with
complex geometries that are submicron or nanoscale in size. Thirdly, the magnetic
response of metals tends to saturate at high frequencies due to the permittivity
approaching zero[38]. This limits the realization of plasmonic metamaterial to visible and
ultra-violet frequencies.
1.6 Resonant Dielectric Metamaterials
The above-mentioned problems associated with plasmonic metamaterials give us
a reason to consider alternative routes such as switching the metamaterial constituents to
dielectrics, where the intrinsic material loss can be much less. Unlike the resonance in
metal structures which is due to the conduction current on the surface, Mie resonances in
dielectric particles result in magnetic and electric dipole like fields via displacement
current. In the case of spheres or cubes, the lowest resonance frequency corresponds to a
magnetic dipole and the second resonance corresponds to an electric dipole (Fig. 1.7). If
an array of these particles is assembled into unit cells, these resonances can be used to
15
tailor the effective permeability ( ) and permittivity ( ) of the composite.
Figure 1.7. Illustration of Mie resonances in dielectric cubes. The curve shows the
scattering cross-section (SCS) of a Si nano-cube with a length of 500 nm. The two peaks
in the SCS plot correspond to a magnetic and electric dipole resonance, respectively.
16
Figure 1.8. Schematic showing an array of dielectric spheres with permittivity 2
embedded in a host medium with permittivity 1 [39].
The first theoretical prediction of negative effective permeability ( ) and
permittivity ( ) in dielectric materials was provided by Lewin back in 1946. In his paper
“The Electrical Constants of a Material Loaded with Spherical Particles” [39], he
investigated the optical response of a dielectric sphere array with a permittivity of 2
embedded in a dielectric host medium with a permittivity of 1 . By rigorously applying
the Mie scattering theory and combining it with Clausius-Mossotti effective medium
theory, he predicted the condition for 0eff to be,
31
2
f
e
f
e
F b
F b
(1.7)
where,
17
2
' '
0 2 2
1
2
2 sin cos,
1 sin cos
,
,
r r
e
F
k a
b
(1.8)
and f is the filling fraction of the dielectric spheres. A similar condition holds for
0eff .
Figure 1.9. (a) Schematic of a silicon nano-rectangle antenna with length Lx, width Ly
and height Lz. (b) The scattering cross-sections of the silicon nano-antenna as a function
of the antenna length Lx. The solid lines represent electric dipole resonance, and the
dashed line represent the magnetic dipole resonance.
Mie resonances occur in any dielectric particle and their ordering and spectral
location can be controlled by the size or shape of the resonator. The advantage of
dielectrics over their metallic counterparts is that they allow the frequency of operation to
be scaled to arbitrary wavelengths and they experience reduced optical absorption,
provided a transparent dielectric is used as the resonator. Furthermore, in the case of
spheres or cubes, isotropic optical properties are possible while still employing simple
18
unit cell geometries, opening the door to scalable 3D metamaterials.
Experimental demonstrations and designs of dielectric metamaterials have
primarily been limited to the microwave frequency range where constituent materials
with permittivity in excess of ɛ = 100 are available, allowing deep sub-wavelength unit
cells[40]. In the limit of low constituent permittivity, the unit cell’s resonance position
becomes comparable to the excitation wavelength, invalidating homogenization.
Dielectric metamaterials have been shown to exhibit many of the same properties as
metallic metamaterials including high frequency magnetism and a negative refractive
index[41]–[44]. It is important to note that to achieve the more complicated negative
index response it is necessary to overlap both an electric and magnetic resonance. Despite
these proposals, experimental realizations of dielectric based metamaterials at optical
frequencies have been slow to materialize. At the inception of the research outlined in
this thesis, the highest frequency of operation which has been experimentally
demonstrated is 40 THz which was achieved using high index tellurium cubes as the unit
cell. However, in this demonstration a single resonator was used in the unit cell, resulting
in no overlap in the electric and magnetic response[45]. Researchers have also begun to
examine the magnetic response and Fano resonances present in dielectric particles at
optical frequencies[46], though no metamaterials have been formed from them until the
inception of this thesis.
1.7 Organization of the Thesis
In this thesis, I present my efforts to realize resonant dielectric metamaterials at
optical frequencies. Such developments will hopefully lead to novel compact optical
19
devices with superior performance and ultimately practical applications. In particular, I
will present how artificially-designed dielectric nano-structures can be applied for
efficiently controlling light emission, propagation, bio-sensing, and enhancing nonlinear
light-matter interaction with greatly improved performance over plasmonic devices.
Chapter 2 describes the first experimental realization of a low-loss 3D zero-index
metamaterial (ZIM) with all-dielectric components at optical frequencies. A composite
engineered structure exhibiting an effective refractive index of zero is designed and
fabricated based on low-loss silicon (Si) material. Due to the isotropic nature of the ZIM,
I demonstrate the ability to control the spontaneous emission of light by embedding
quantum dot emitters within the ZIM and observing directional and enhanced light
emission.
In Chapter 3, I transition the focus from bulk 3D dielectric metamaterials to
ultrathin 2D dielectric metasurfaces. I show that engineered dielectric nano-antennas
exhibiting Mie resonances can be used in place of plasmonic antennas to drastically
modify the phase of light while maintaining near-unity efficiency. I experimentally
demonstrate highly efficient broadband linear polarization conversion and optical vortex
generation with a silicon-based meta-reflectarray.
Chapter 4 is a study of the possibility of using dielectric nanoantenna arrays to
mimic electromagnetically induced transparency (EIT) and to realize Fano-type
resonances with ultrahigh quality factors. This is realized by forming a periodic array of
coupled electric and magnetic dipole antennas and the associated minimized non-
radiative decay of light. Combining the sharp resonance with strong field confinement in
its surrounding medium, I show that such a device can be an ideal platform for bio-
20
sensing.
In Chapter 5, I further investigate the nonlinear light-matter interaction in the
Fano-resonant dielectric metasurface. The metasurface results in strong near-field
enhancement within the volume of the silicon resonator while minimizing two photon
absorption, leading to greatly enhanced efficiency and saturation power for third
harmonic generation. The enhanced nonlinearity, combined with a sharp linear
transmittance spectrum, results in transmission modulation via the Kerr effect with a
large modulation depth.
In Chapter 6, I will discuss one possible way to integrate the concept of Mie
resonances with active material systems such as quantum wells. By overlapping the
electric and magnetic resonances, these hybrid structures can achieve near-unity light
absorption in the quantum wells, leading to greatly enhanced quantum efficiency of a
quantum well-based infrared photodetector.
Finally, Chapter 7 summarizes the highlights of this work and its long term
implications. In the end, I would like to give my perspective on the future of
metamaterials.
21
Chapter 2 3D Dielectric Metamaterials — Zero Refractive Index
2.1 Introduction
Over the past decade, one of the key goals of metamaterial research has been to
realize materials with arbitrary effective refractive index such that we can tailor the
propagation of light at will. Recently, metamaterials with refractive index equal to zero
have drawn particular interest. Waves traveling inside such a medium do not experience
any spatial phase change and the phase velocity approaches infinity, as is illustrated in
Fig. 2.1. These properties can be used for realizing directional emission[47]–[49],
tunneling waveguides[50], large-area single-mode devices[51] and electromagnetic
cloaks[52]. In the past, most work aimed at achieving zero-index has been focused on
epsilon-near-zero metamaterials (ENZs) which can be realized using diluted metals or
metal waveguides operating below cut-off. These studies have included experimental
Figure 2.1. Schematic of light propagation in the air and ZIM, respectively.
22
demonstrations in the microwave[47], [53], mid-IR[54], and visible[55] regimes. ENZ
metamaterials have a permittivity that is near-zero and a permeability of unity, resulting
in a near-zero refractive index; however, since the permeability remains finite, the
relative optical impedance is inevitably mismatched from free-space, resulting to large
reflections from the interface. Impedance matched zero-index metamaterials (ZIMs) in
which both the permittivity and permeability are set to zero eliminate these strong
reflections and have recently been demonstrated at optical frequencies using metal based
fishnet structures. However, fishnet metamaterials do not possess isotropic optical
properties and the use of metals inevitably introduces ohmic loss that will limit the
thickness of the material.
As is discussed in detail in Chapter 1, resonant all-dielectric metamaterials offer
one potential solution to these issues due to the absence of Ohmic loss, and their simple
unit-cell geometries[57]. However, while magnetic modes in high-index particles have
recently been characterized experimentally at optical frequencies[58], [59],
implementations of dielectric metamaterials have been limited to the microwave[42],
[43], [57] and mid-infrared[44] regimes up to the inception of this work.
In this chapter, I detail the first experimental demonstration of an all-dielectric
ZIM operating at infrared frequencies. The design of the metamaterial is based on a
recent proposal reported by Chan et. al.[60] in which it was shown that a metamaterial
made of purely dielectric high-index rods can exhibit a Dirac cone at the point in the band
structure, a feature that is similar to the electronic band structure in graphene[61]. At the
Dirac point, the metamaterial exhibits zero effective permittivity and permeability,
resulting in an impedance-matched ZIM. Experiments at microwave frequencies have
23
demonstrated some of the unique properties arising from an effective index of zero, such
as cloaking and lensing. However, a demonstration at optical frequencies has yet to be
provided. Here, we implement a ZIM at optical frequencies using vertically stacked
silicon rods, allowing access from free space. We demonstrate that the optical ZIM serves
as an angular optical filter while also enhancing the directivity of spontaneous emission
from quantum dot light sources embedded inside the structure. The experimental results,
together with numerical calculations, serve as direct evidence of impedance-matched
near-zero index within the metamaterial.
2.2 Photonic Dirac Cone and Zero Index Design
The design of the ZIM consists of a stack of square cross-section Si rods
embedded in SiO2 with w=t= 260 nm and a= 600 nm, is shown in Fig. 2.2(a). The band
structure is computed for TM polarization with the electric field oriented along the rod
axis and the Dirac cone like dispersion can be observed at the center of Brillouin zone
where two transverse bands with linear dispersion intersect a flat quasi-longitudinal band,
resulting in triple degeneracy, as is shown in Fig. 2.2(b). We utilized field-averaging of
the Bloch modes[62] to retrieve the metamaterial’s effective bulk optical properties (Fig.
2.2c) and simultaneous zero-permittivity and permeability are obtained at the triple
degeneracy frequency of 211 THz (λ0=1422 nm). This response is directly attributable to
a linear combination of electric monopole and magnetic dipole Mie resonances within the
Si rods (inset of Fig. 2.2c), allowing the effective constitutive parameters to be accurately
extracted using effective medium theory[63]. This was confirmed by the excellent
agreement between the extracted propagation vector, acquired using field averaging, and
24
the computed band structure around the triple degeneracy point. Furthermore, the
impedance of the structure is also accurately represented using the effective constitutive
parameters, further supporting the assignment of an effective permittivity and
permeability for the structure. A relatively broadband impedance matched low-index
region is present around the zero-index point and over the frequency range from 215 THz
to 225 THz there exists only one propagating band, TM4, which allows us to define an
effective index of refraction for the structure for off-normal angles of incidence. The
isofrequency contours (IFCs) over this frequency range are shown in Fig. 2.2(d) and it
can be observed that they maintain a nearly circular shape indicating that the material
maintains a relatively isotropic low-index response for TM-polarized light over this
bandwidth. This all-angle response is critical for preserving the unique physics associated
with low- or zero-index materials such as directionally selective transmission and
emission from within the material. It should be noted that in a perfectly homogeneous
zero-index metamaterial, the flat longitudinal band is not accessible with TM-polarized
light.
25
Figure 2.2. (a) Diagram of the ZIM structure with a unit cell period of a = 600 nm and w
= t = 260 nm. (b) Band diagram of uniform bulk ZIM (infinitely thick) for TM
polarization. Dirac cone dispersion is observed at the Γ point with triple degeneracy at
211 THz. The shaded area denotes regions outside the free-space light line. (c) Retrieved
effective permittivity and permeability of the bulk ZIM acquired using field-averaging.
The inset shows the electric and magnetic fields within a single unit cell at the zero-index
frequency indicating a strong electric monopole and magnetic dipole response. (d) IFC of
the TM4 band. The contours are nearly circular (i.e., isotropic) for a broad frequency
range and increase in size away from the zero-index frequency indicating a progressively
larger refractive index.
2.3 Fabrication and Optical Characterization
The fabricated ZIM consists of 200 µm long Si rods which support electric and
magnetic resonances and the rods are separated by a low index material, silicon dioxide
(SiO2) (Fig. 2.3). One of the consequences of a low or zero-index is that light will not be
26
guided using a conventional slab waveguide and thus the material must be fabricated for
free-space access when metal or other reflective cladding layers cannot be utilized. To
realize a free-space accessible material, fabrication began with a multilayer stack of 11
alternating layers of α-Si (ε=13.7, 260 nm thick) and SiO2 (ε=2.25, 340 nm thick)
followed by a patterning and reactive-ion etching (RIE) (details in the Supporting
Material). In the final step, poly(methyl methacrylate) (PMMA) (ε=2.23) was spin-coated
onto the sample to fill the air gaps. Figure 2.3(e) shows a cross-section of the fabricated
structure before final PMMA spin-coating and Figure 2.3(f) depicts a sample after spin-
coating. A total of 5 functional layers (Si / SiO2 pairs) results in a metamaterial with a
thickness of 3 μm, about twice the free-space wavelength at the zero-index point.
Figure 2.3. (a)-(d) Schematic of the detailed fabrication steps. (e)-(f) SEM image of the
fabricated sample (e) before and (f) after PMMA filling.
27
The detailed fabrication steps of the ZIM are outlined in Fig. 2.3(a)-(d). We
developed a unique low pressure chemical vapor deposition (LPCVD) process to deposit
11 alternating layers of α-Si (260 nm) and SiO2 (340 nm) during a single process run on
a 4 inch quartz wafer. The LPCVD tool used was a horizontal tube furnace. A quartz
caged boat was used to contain the wafer to improve cross wafer uniformity. Deposition
temperature was 550°C and process pressure was 300mTorr and both were held constant
throughout the deposition of both films. Process gases were introduced into the tube
furnace via mass flow controllers. The α-Si layer was deposited by flowing 50sccm’s of
100% SiH4. The SiO2 layer was deposited by flowing 85sccm’s of SiH4 and 120sccm’s
of O2. A brief N2 purge was introduced between layers. This alternating process was
repeated until the desired number of layers was deposited.
A hard metal etch mask was patterned using electron beam lithography (Raith
and/or Jeol) and deposition of 50 nm chromium (Cr) followed by lift-off. To avoid
surface charging detrimental effects, electron beam sensitive resist (ZEP520A and/or
PMMA) was coated with a 10 nm Cr charge dissipation layer to be chemically removed
prior to the exposed resist development. A fluorine based reactive ion etching (RIE)
recipe was developed in an Oxford Plasma Lab tool to etch the multilayer sample by
alternating the recipe for the Si and SiO2 layers. The final structure has a 10:1 aspect ratio
with respect to the total height and gap width between the rods. The base etch recipe
involved 100 W RF power, 2000 W ICP power with C4F8 and O2 gas flows for the SiO2
layers and 80 W RF, 1200 W ICP with C4F8, SF6, O2 and Ar gas flows for the α-Si layers.
The oxide had a positive slope as we etched down to subsequent layers underneath.
Starting with the base recipe for the upper layers, the subsequent SiO2 layers were etched
28
more aggressively with increasing depth. This was accomplished by changing the ratio of
C4F8 and O2 gas-flow which provided less passivation to the side walls during etching.
The base Si etch recipe resulted in straight side walls until we reached the bottom most
layer. The bottom most oxide and Si layers were etched with the most aggressive recipes
and the top layers were protected by additional passivation steps. The metamaterial’s
internal structure was characterized by imaging the edge profile after milling cross-
sections inside the array using focused ion beam milling (FIB). During all imaging, a thin
layer of Cr was deposited on the sample to provide a conducting surface.
We made sure that PMMA, which was spin-coated on the sample after the RIE
process, filled in the gaps completely in order to provide a background with the same
permittivity as the SiO2 spacer layers. The sample with a drop casted PMMA film was
placed in an evacuated desiccator to remove air bubbles and this process was followed by
spinning and soft baking (120 degrees for 2 minutes) twice and reflowing at 300˚ C for 2
minutes to reach the desired thickness. The final structure was cross-sectioned with FIB
milling at multiple locations to confirm the complete filling.
In order to gauge the agreement with the simulated material properties,
transmittance of the fabricated ZIM was acquired by illuminating the sample with
normal-incident white light with the electric field oriented along the Si rod axis (Fig. 2.4).
The simulated and measured transmittance show excellent agreement in spectral shape,
though the experimentally obtained curve has a lower amplitude that is likely due to non-
uniformity in rod width at the edges of the sample as well as surface roughness. The
measured spectrum shows a peak transmission of 80% at 1405 nm, the spectral position
corresponding to the impedance-matched low-index point. A dip in transmission also
29
occurs at 1460 nm, corresponding to the metallic region of the sample.
Figure 2.4. Experimental (red) and theoretical transmittance (dotted blue) curves of the
ZIM (200 x 200 µm2 total pattern area). Regions corresponding positive index, metallic
properties, and negative index are denoted with blue, grey, and yellow shading,
respectively.
While these bulk parameters are used as a design guide, the fabricated
metamaterial has both a finite thickness as well as non-uniform rod sizes and will thus
deviate somewhat from the bulk parameters. To better understand the optical response of
the fabricated metamaterial, full-wave finite-difference time-domain (FDTD) simulations
were performed and S-parameter retrieval[64], [65] was used to compute the effective
optical properties (Fig. 2.5a,b). Due to the non-uniform rod size, the impedance matched
point in fabricated structure is shifted to 1400 nm corresponding to 0.12eff eff effn μ ε .
30
It can also be observed that a metallic region is opened from 1430 nm to 1460 nm in
which the permittivity is negative while the permeability remains positive. The
metamaterial exhibits a negative index region beginning at 1460 nm though this region
cannot be assigned with optical properties for arbitrary angles of incidence due to
presence of the quasi-longitudinal band which is accessible at large incident angles.
Figure 2.5. (a) Effective permittivity and permeability of the fabricated ZIM obtained
using S-parameter retrieval. Regions corresponding positive index, metallic properties,
and negative index are denoted with blue, grey, and yellow shading, respectively. (b)
Effective refractive index of the fabricated structured obtained using S-parameter
retrieval.
One of the most fascinating properties of isotropic low-index materials is that
light incident from free-space is only transmitted over a narrow range of incidence
angles. This effect is a direct consequence of phase matching at the interface which
requires that the wavevector along the interface be conserved. As illustrated with the IFCs
depicted in Fig. 2.6(a), in a low-index metamaterial, the wavevector is restricted to
extremely small values causing light incident at high angles ( 𝑦,0 > | 𝑍𝐼𝑀| ) to be
31
reflected while near-normal incident light is transmitted ( 𝑦,0 < | 𝑍𝐼𝑀|). This effect is
evident when examining the simulated transmittance with regard to wavelength and angle
of incidence (Fig. 2.6b) for the fabricated ZIM. The material exhibits near-zero
transmission at off-normal incident angle within the positive index band centered at 1400
nm, with improving angular confinement in transmission as we approach the zero-index
point. The presence of the quasi-longitudinal band within the negative index region
(𝜆0~1475 nm) is also apparent, allowing transmission at large incident angles.
To experimentally verify that the fabricated ZIM preserves these features, light
transmitted through the sample was imaged in the Fourier plane. Illumination was
provided by a femtosecond synchronously pumped optical parametric oscillator
(Coherent, MIRA OPO) that was focused with a large numerical aperture objective
(NA=0.85), providing incident angles up to 58.2°. The acquired Fourier images (Figs.
2.6. c-g) show confinement of light along the y-axis of the material which is in the
direction of in-plane periodicity. Within the low index region between 1400 nm and 1475
nm, tighter confinement of ky is observed with progressive lowering of the refractive
index, in agreement with the simulated data. Confinement is absent in the x-direction due
to the fact that the electric field is no longer directly along the rod axis for these incident
angles. The directional filtering of transmission demonstrates that a nearly isotropic low-
index for TM-polarized light is indeed preserved within the fabricated metamaterial.
32
Figure 2.6. (a) IFCs of air and a low-index metamaterial illustrating angularly selective
transmission due to conservation of the wave vector parallel to the surface. (b) Simulated
angle and wavelength-dependent transmittance of the fabricated structure. (c)-(f) Fourier-
plane images of a beam passing through the fabricated ZIM structure within the low
index band. Angularly selective transmission can be observed in the y-direction due to the
low effective index. Along the x-direction, angular selectivity is not preserved due to the
one-dimensional nature of Si rods. (g) Fourier-plane image of the illumination beam
demonstrating uniform intensity over the angular range measured.
2.4 Directive Quantum Dot Emission
An additional consequence of the near-zero spatial phase change is that
incoherent isotropic emitters placed within the ZIM will tend to emit coherently in the
direction normal to the air/ZIM interface[47]–[49]. To demonstrate this effect, we placed
lead sulfide (PbS) semiconductor quantum dots (QDs) within the ZIM to act as the
emitter. The QDs had a luminescence peak centered at 1420 nm and a full width at half
maximum of 172 nm. The QDs were sandwiched between two PMMA layers within the
33
ZIM, and were excited with a tightly focused 1064 nm laser beam. The Fourier-plane
images (Fig. 2.7c-d) from both an unstructured PMMA/QD film and QDs placed within
the metamaterial show good angular confinement in the y-direction and an over two-fold
increase in intensity emitted normal to the interface from the ZIM compared to the
unstructured case. The increase in emission normal to the interface is a result of the
uniform phase distribution within the ZIM, leading to constructive interference from
emitters throughout the material[55], further supporting the realization of a near-zero
refractive index. The constructive interference of multiple emitters is in competition with
the reduced optical density of states associated with the low-index response. For instance,
if the number of emitters is reduced to one, the emitted power in air will be greater than
the ZIM in all directions. However, as expected for constructive interference within the
material, the far-field intensity of waves propagating normal to the interface is
proportional to the number of emitters squared. We also note that although the
luminescence peak of the QDs matches the low-index band of fabricated ZIM structure
quite closely, parts of the emission fall beyond the low-index band, resulting in slightly
lower angular confinement compared with the transmission data.
34
Figure 2.7. (a) Schematic of laser-pumped QD emission from within the ZIM structure.
(b) Photoluminescence (PL) spectrum of PbS quantum dots (Evident Technology) used in
the main text. The emission peak appears at 1425 nm, with a full-width at half-maximum
of 172 nm. The blue-, gray- and yellow-shaded region corresponds to positive index,
metallic properties, and negative index as acquired from S-parameter retrieval. The dip of
measured luminescence spectrum at around 1380 nm is due to the water absorption line.
(c) 2D Fourier-plane images of quantum dot emission on the substrate, intensity is scaled
by two times. (d) 2D Fourier-plane images of QD emission within the ZIM.
2.5 Conclusion
To summarize Chapter 2, we have experimentally demonstrated the first all-
dielectric zero-index metamaterial at optical frequencies, which exhibits a nearly
isotropic low-index response for a particular polarization, resulting in angular selectivity
of transmission and spontaneous emission. The realization of impedance-matched ZIMs
at optical frequencies opens new avenues towards the development of angularly selective
35
optical filters, directional light sources and large-area single-mode photonic devices.
Furthermore, the advent of all-dielectric optical metamaterials provides a new route to
developing novel optical metamaterials with both low absorption loss and isotropic
optical properties.
36
Chapter 3 2D Dielectric Metasurface — Meta-Reflectarray
3.1 Introduction
While bulk 3D metamaterials are preferred for applications such as enhancing
light emission and invisibility cloaking, there are other circumstances where efficient
light manipulation over a small distance (for example, with an ultrathin 2D meta-surface)
can be beneficial. Achieving full control over light propagation is an ever present issue in
modern day optics. In order to realize such control it is necessary to create devices that
allow 0 to 2π phase modulation and / or devices that allow control over the amplitude of
light. In conventional optical elements such as birefringent waveplates and lenses, a
significant propagation distance is needed to acquire disparate phase accumulation for
different polarizations or spatial regions of the beam, thus requiring thick materials that
are difficult to integrate into compact platforms[66]. One solution to this issue is the use
of reflect and transmit-arrays, originally developed at radio frequencies, that allow one to
control the amplitude and phase of light using a single, or several, layers of ultra-thin
antennae[67], [68]. By changing the geometry of the antenna as a function of position,
these arrays allow spatial control over the phase of light. Recently, similar materials,
deemed metasurfaces, have been developed at optical frequencies[23]. Metasurfaces
typically utilize asymmetric electric dipole resonances to allow 0 to 2π phase control for
the cross-polarized scattered light. As in transmitarrays, varying the geometry of the
resonator as a function of position allows arbitrary control of the phase front of light
using a subwavelength-thin film and has led to demonstrations including anomalous
refraction[23], [69]–[72], quarter and half waveplates[24], [73], lensing[74]–[76], and
37
manipulation of orbital angular momentum[77], [78].
One of the drawbacks of plasmonic metasurfaces is that they typically suffer from
low efficiency due to weak coupling between the incident and cross-polarized fields.
Methods to increase efficiency include the use of overlapped electric and magnetic
resonances[79] as well as the use of thicker metasurface sheets[80], though both of these
proposals require materials with increased complexity. One can also employ antennae
working away from their resonance positions to realize quarter-waveplates with
polarization conversion efficiencies of close to 50% over large bandwidths[81]. In
another approach it was shown that an array of metallic antennae, in combination with a
reflective ground plane, can achieve efficiencies of up to 80% for anomalous
reflection[71], [76], [82] and linear polarization conversion[73] by introducing multiple
reflections within the film. While this design avoids complexity, the use of metallic
antennae still limits metasurfaces from achieving unity efficiency at optical wavelengths
due to the Ohmic losses in metal[71].
Dielectric metasurfaces composed of a periodic or spatially-varying resonant
dielectric antenna array may again offer an alternative by greatly reducing the non-
radiative (material) loss. Closely related to this concept are high-contrast gratings (HCGs)
and artificial dielectrics. In HCGs, Mie resonances are used to control the phase of
transmitted or reflected light at a surface. HCGs have been used to achieve surfaces with
near-unity reflection for applications such as mirrors in vertical-cavity surface-emitting
lasers[86], quarter waveplates[87], and optical elements with spatial phase variation such
as lenses[88], [89] and spiral phase plates[90]. However, one of the drawbacks of this
approach is that it is difficult to achieve full 2π phase control while preserving near-unity
38
reflectance with a single layer grating, an issue that becomes more restrictive as the index
of the resonator is reduced. In artificial dielectrics[91]–[93], high index dielectric
structures are patterned with deep sub-wavelength spacing to achieve a gradient index
surface along the surface. High diffraction efficiency can be realized with such surfaces,
however, due to the lack of strong resonances and thus low index contrast, the thickness
of the surface must be greater than the free-space wavelength to acquire a 0 to 2π phase
shift. This results in the need to fabricate structures with relatively high aspect ratios
which can be challenging.
In this chapter, we demonstrate a broadband dielectric meta-reflectarray linear
polarization convertor by utilizing structured silicon (Si) cut-wire resonators placed
above a silver ground plane. The meta-reflectarray utilizes Mie resonances in the Si
resonators and multiple reflections from the silver mirror. The multiple reflections relax
the required phase delay upon a single pass through the resonator layer, mitigating the
tradeoff between phase control and efficiency present in single layer HCGs. This allows
the meta-reflectarray to serve as a half-waveplate with near-unity reflectance and over
98% polarization conversion efficiency across a 200 nm bandwidth. Furthermore, by
varying the resonator dimensions, broadband 2π phase control of the reflected cross-
polarized light can be achieved while maintaining high conversion efficiency, opening the
door to ultra-compact lenses and phase plates at optical wavelengths.
3.2 Broadband Linear Polarization Conversion
A schematic of the polarization converter is illustrated in Fig. 3.1(a). It is
composed of an array of Si cut-wires and a silver ground plane, with a low index PMMA
39
spacer in between. Device fabrication began with depositing a 380-nm-thick amorphous
Si (n=3.7) thin film on quartz. The cut-wires were then created using electron beam
lithography and reactive-ion etching. PMMA (n=1.48) was then spin-coated onto the
sample and planarized to serve as the low index dielectric spacer and a silver film was
deposited on top, serving as the reflective mirror. The SEM image of the fabricated
sample is shown in Fig. 3.1(b).
Figure 3.1. (a) Schematic of the meta-reflectarray with a unit cell period of p = 650 nm, a
= 250 nm, b= 500 nm, t1 = 380 nm and t2 = 200 nm. In the fabricated sample the
resonators are embedded in PMMA and a quartz wafer caps the resonators. (b) SEM
image of the sample before spin-coating PMMA and depositing the silver film.
40
Figure 3.2. (a) Schematic of the polarization conversion measurement set-up. (b)
Measured and simulated reflectance for co- and cross-polarized light. (c) Polarization
conversion efficiency of the device. The shaded regions indicate the wavelength range
where experimental measurements were not possible due to low detector quantum
efficiency (d) Schematic of the decomposition of linearly polarized incident and reflected
light. (e)-f) Reflectance and phase for x and y polarized light demonstrating near-unity
reflection and a broadband π phase shift.
To experimentally characterize the performance of the polarization converter, we
used a supercontinuum light source (Fianium SC400), incident normal to the sample
surface with the polarization along the x-axis, which is tilted 45° with respect to the Si
cut-wire axis. Two linear polarizers were employed in front and after the sample to
measure the reflectance of the same polarization state as that of the incident wave, ,
and that of the perpendicular polarization , as illustrated in Fig. 3.2(a). All
reflectance measurements were normalized to the reflectance measured from a silver
mirror. Figure 3.2(b) shows the measured reflectance for both polarizations and the
2
cor
2
crossr
41
corresponding polarization conversion rate (PCR), defined as , is
shown in Fig. 3.2(c). The experimental measurements demonstration that the PCR
remains above 98% from 1420 nm to 1620 nm, and the cross-polarized reflection remains
above 97% over this bandwidth, in good agreement with the simulation. Measurements
beyond 1620 nm were not possible (shaded region in Figs 3.2b-c) due to the low quantum
efficiency of the spectrometer’s indium gallium arsenide detector and reduced light
source intensity at long wavelengths. However, the numerical simulation predicts that
90% PCR extends out to 1720 nm and given the good agreement with theory, we expect
the experimentally achievable efficiency to also be preserved over this range.
To better understand the response of the meta-reflectarray, the incident light,
which is linearly polarized along the x-direction, can be decomposed into two
perpendicular components, u and v which correspond the short and long axis of the
resonator, respectively (Fig. 3.2d). The numerically simulated reflection amplitude and
phase for a resonator array illuminated with polarization along these axes are shown in
Figs. 3.2(e),(f). It can be observed that the reflection amplitudes in both polarizations are
close to unity while the relative phase retardation is roughly π throughout the wavelength
range where the linear polarization conversion occurs, leading to a 90° polarization
rotation when light is incident with polarization along the x or y-axis of the sample.
The high conversion efficiency can also be understood by modeling the field
evolution upon multiple reflections within the low-index spacer layer, resulting in
constructive and destructive interference of the cross and co-polarized light,
respectively[73], as is shown in Fig. 3.3.
2 2 2
cross cross cor r r
42
Figure 3.3. (a) Schematic of the multiple reflections. (b) Comparison between the
calculated reflected field from multiple reflections and the simulated overall reflected
field.
In this model, the resonator array, the PMMA spacer, and the metal ground plane
are each treated as an individual layer. For the resonator layer, light incident onto the top
surface can couple into the resonators and then radiate back to the environment with the
amplitude and phase being modified differently for co- and cross-polarized fields. The
layer of resonators can then be regarded as an effective layer and the light being re-
radiated can be treated as being reflected or transmitted. The complex reflectivity and
transmissivity from the resonator layer is obtained from FEFD simulations from an array
of resonators embedded in PMMA without the metal ground plane. The reflectivity and
transmissivity are expressed as rr and t where =0 for co-polarized fields and ρ = 1 for
cross-polarized fields. Based on the multiple reflection model, the reflected field,', jE (j
represents the jth pass), from each individual pass is given by
43
', 1 '
2 2' 0, 2 0 1 0 0
' 1, 2 1 0 0 0
2 22 2 2 2
' 0, ,( 3) 0 2 0 1 1 2 0 1 1 0 2 0
0 0( ) ( )
( ) exp( 2 )
exp( 2 )
(
j inc
j inc m
j inc m
j jl j l l l j l l l
j j inc j j j
l ll even l even
E E r
E E t t i k n d r
E E t t i k n d r
E E t C r r t C r r t t C r
2
2 1
1 0 0
1( )
2 2 22 2 2 2 2 1
' 1, ,( 3) 0 2 0 1 1 2 0 1 1 0 2 0 1 0 0
1 1 0( ) ( ) ( )
) exp( 2 )
( ) exp( 2 )
jj l l j
m
ll odd
j j jl j l l l j l l l j l l j
j j inc j j j m
l l ll odd l odd l even
r i k n d r
E E t C r r t C r r t t C r r i k n d r
(3.1)
where incE is the incident electric field, 0k is the free space wave number, 0n is the
refractive index of PMMA, d is the spacer thickness, l is an integer number smaller than
(j-2) and represents the number of times that the polarization is rotated upon reflection at
the bottom surface of resonator layer in the jth pass. As a field being cross-polarized
twice will return to a co-polarized field, the requirement for the jth path,', jE
to be co-
polarized is that 1 appears an even number of times in the equations. The same is true
for cross-polarized field where 1 can only appear an odd number of times. The overall
reflection for both co- and cross-polarization is the sum of individual passes' ', j
j
E E .
The simulated overall reflected field and the calculated sum of the reflected field of each
pass are plotted in Figure B.3(b). The result from the FEFD simulation and the
calculation shows good agreement in both co- and cross-polarization, which corroborates
the theory.
3.3 Broadband Optical Vortex Generation
More interestingly, by properly engineering the cut-wire geometry, a 0 to 2π phase
shift can be achieved for the cross-polarized reflected light with near-unity efficiency.
44
This is in contrast to plasmonic V-shaped antenna based metasurfaces, where the majority
of scattered light remains in the ordinary component (co-polarized), resulting in low
signal-to-noise ratio (SNR)[23]. The 2-dimensional colormap of the numerically
simulated reflectance, , and phase, , of the meta-reflectarray with varying Si
cut-wire dimensions at a fixed wavelength of 1550 nm, are plotted in Figs. 3.4(a),(b).
These simulations were performed using a finite-element frequency-domain solver (CST
Microwave Studio) with periodic boundary conditions. It can be observed that there is a
region of high reflectance in which four antenna dimensions were chosen (circles in Fig.
3.4a,b) to provide an incremental phase shift of π/4 for cross-polarized reflected light. By
simply rotating the structures by 90°, the additional π phase shift can be attained for
realizing full 2π coverage while maintaining near-unity efficiency.
An additional feature of this reflectarray is that it can maintain high efficiency
over a wavelength range of ~100 nm within the telecommunications band as
demonstrated by the simulated reflection amplitude and phase for the eight resonators as
a function of the incident wavelength between 1500 nm and 1600 nm (Fig. 3.4d-e).
Within this range, the cross-polarized reflectance remains above 75% with the greatest
drop occurring for resonators 1 and 5 at long wavelengths. However, despite this drop,
the average reflectance is 93.6% across this bandwidth. The phase gradient is calculated
by taking resonator 1 as a reference at each wavelength and setting its phase advance to
zero. Across the l00 nm bandwidth it can be seen that the phase gradient across the
resonators remains linear, ensuring the designed phase profile is maintained.
2
crossr cross
45
Figure 3.4. Simulated cross-polarized reflection (a) magnitude and (b) phase for
resonators with varying geometry at a fixed wavelength of 1550 nm. The unit cell period
is set as 650 nm and the PMMA spacer thickness is set to 150 nm. (c) Schematic of eight
resonators that provide a phase shift from 0 to 2π. The dimension of resonators 1-4 are 1)
a=200nm, b=425nm; 2) a=225nm, b=435nm; 3) a=250nm, b=450nm; 4) a=275nm,
b=475nm. Resonators 5-8 are simply rotated by 90° with respect to resonators 1-4.
Simulated cross-polarized reflection (d) amplitude and (e) phase for arrays of resonators
1-8 as a function of the incident wavelength. The phase delay of array 1 is set to 0 for
each wavelength to serve as a reference.
In order to validate the performance of a variable phase meta-reflectarray, we
fabricated a sample with a spiral phase profile ranging from 0 to 2π with a phase
increment of π/4 along the azimuthal direction (shown in Fig. 3.5a-b). The design is
based on the 8 Si cut-wire resonators modeled in Fig. 3. This particular phase profile
46
leads to the generation of a Laguerre-Gaussian beam with a theoretical cross-polarized
reflectance that is above 94.5% for each section of the reflectarray at the center
wavelength of 1550 nm. The Laguerre-Gaussian beam has a helical wavefront with a
phase singularity in the center characterized by an azimuthally dependent phase term,
, where l represents the topological charge, which was chosen as l = 1, and is
the azimuthal angle[94]. This optical vortex beam carries orbital angular momentum,
making it a platform for investigating fundamental physical phenomenon such as spin-
orbit interaction in photonic systems[77], [78], and such beams have various applications
in optomechanics[95] and information processing[96]–[99].
The evolution of the vortex beam as a function of incident wavelength was
measured by illuminating the sample with a linearly polarized and collimated tunable
continuous wave diode laser. A linear polarizer oriented 90° with respect to the
illumination polarization was placed in front of the camera to filter out any co-polarized
light. Images of the reflected cross-polarized beam are shown in Figs. 3.5(c)-(e) and have
the characteristic intensity minimum at the center which is a direct consequence of self-
cancel-out associated with the corkscrew shaped beam. The reflected beam was also
measured using a Michelson interferometer with the generated vortex beam and the co-
propagating Gaussian beam in the sample and reference arm, respectively. The dislocated
fringe and spiral shape phase patterns are clearly observable when the two beams are
tilted and collinear with respect to each other, respectively, as illustrated in Figs. 3.5(f)-
(k). In order to qualitatively gauge the conversion efficiency of the meta-reflectarray, the
linear polarizer place before the camera was removed, resulting in the images shown in
Figs. 3.5(l)-(m). It can be observed the spiral patterns remain largely unaffected, though
exp( )il
47
there is moderate noise in the center of the pattern which is due to the imperfections in
the cut-wire arrays leading to increased co-polarized reflection.
Figure 3.5. (a) Optical microscope image of the fabricated spiral phase plate composed
of eight sections of Si cut-wires, providing an incremental phase shift of π/4. (b) SEM
image showing the cut-wires at the center of the reflectarray. (c-e) Experimentally
measured intensity profiles of the generated vortex beam with topological charge l=1.
The wavelengths of incident light are (c) 1500 nm, (d) 1550 nm, and (e) 1570 nm. (f-h)
Interference pattern of the vortex beam and the co-propagating Gaussian beam when the
beam axes are tilted with respect to one another. (i-k) Interference pattern of a vortex
beam and a Gaussian beam which have collinear propagation. In (c-k) a linear polarizer is
placed in front of the camera to filter out co-polarized light. (l-m) Interference pattern of
the vortex beam and the Gaussian beam in the absence of the linear polarizer.
Lastly, one important aspect that remains to be explored is the role of coupling
48
between the resonators in the array. This has important ramifications for using this type of
meta-reflectarray for realizing short focal length lenses, in which dissimilar resonators are
placed adjacent to one another. To explore the role of coupling, we modeled a surface in
which the 8 resonators from Fig. 3.4, each with a unit cell size of 650 nm x 650 nm, were
placed adjacent to one another forming a linear phase gradient over a supercell with
length S = 5.2 µm. Based on the generalized Snell’s law[23], the surface should exhibit
an anomalous reflection peak at an angle of , where n is the
background index, equal to the index of quartz / PMMA (n = 1.5) in our case, and θi is
the incident angle. Numerical simulations were performed to verify the meta-reflectarray
performance by illuminating the array at normal incidence (θi = 0°) with a Gaussian beam
with a waist size of 7 µm and wavelength of 1550 nm. The cross-polarized reflected field
is plotted in Fig. 3.6(a) and demonstrates a well-defined phase front while the far-field
scattered intensity was collected for both co- and cross-polarized reflection and is plotted
as a function of scattered angle in Fig. 3.6(b). The peak cross-polarized scattering angle
matches well with the theoretical angle of θr = 11.5° (dashed line) and the diffraction
efficiency of the +1 diffraction order is 83% with the major source of inefficiency arising
from light remaining in the 0th
order co-polarized beam. The slight reduction in
conversion efficiency, compared to the spatially homogenous arrays, indicates that
coupling between resonators plays a role in the response and must be taken into account
when designing sharp phase gradients, for applications such as lensing, when dissimilar
resonators are placed next to each another.
1
0sin [( / ) sin( )]r inS
49
Figure 3.6. (a) Electric field plot of the meta-reflectarray illumined with a normally
incident x-polarized Gaussian beam with a wavelength of 1550 nm and waist of 7µm.
The metasurface is composed of the 8 Si cut-wire resonators from Fig. 3 with a unit cell
period of 650 nm. (b) Far-field scattered light as a function of angle for both co- and
cross-polarizations. The dotted line corresponds to the solution of the generalize Snell’s
law and matches well with the full-wave simulation.
3.4 Conclusions
To summarize chapter 3, we have experimentally demonstrated broadband linear
polarization conversion and optical vortex beam generator by employing a meta-
reflectarray based on dielectric antennae. Replacing plasmonic antennae with their
dielectric counterparts allows loss to be reduced and bandwidth to be increased due to
50
lower dispersion. The tradeoff is that dielectric based metasurfaces will invariably have a
slightly larger unit cell size at optical frequencies due to the lack of high index materials
which will limit applications requiring off-normal incidence or large in-plane wavevector.
However, as shown here, this is not a significant limitation for polarization control or in
realizing reflective phase plates for complex beam formation and lensing.
51
Chapter 4 2D Dielectric Metasurface — Analogue of Electromagnetically Induced
Transparency
4.1 Introduction
In addition to controlling the wavefront of light, 2D dielectric metasurfaces can
also be used to dramatically modify the far-field spectroscopic features of light. One
possibility is to use the dielectric metasurface to mimic electromagnetically induced
transparency (EIT), creating ultra-sharp resonances in its transmission spectrum for
application such as bio-sensing and active light modulation.
EIT is a concept originally observed in atomic physics and arises due to quantum
interference resulting in a narrowband transparency window for light propagating through
an originally opaque medium[100]. This concept was later extended to classical optical
systems using plasmonic metamaterials[101]–[109], among others[110], [111], allowing
experimental implementation with incoherent light and operation at room temperature.
The transparent and highly dispersive nature of EIT offers a potential solution to the
long-standing issue of loss in metamaterials as well as the creation of ultra-high quality
factor (Q-factor) resonances, which are critical for realizing low-loss slow light
devices[101], [109], [112], [113], optical sensors[114], [115] and enhancing nonlinear
interactions[116].
The classical analogue of EIT in plasmonic metamaterials relies on a Fano-type
interference[117], [118] between a broadband “bright” mode resonator, that is accessible
from free space, and a narrowband “dark” mode resonator which is less-accessible, or
inaccessible, from free-space. If these two resonances are brought in close proximity in
52
both the spatial and frequency domains, they can interfere resulting in an extremely
narrow reflection or transmission window. Due to the low radiative loss of the dark
mode, the Fano resonance can be extremely sharp, resulting in complete transmission,
analogous to EIT[101], [103], [108], [109], [112], [113], [119]–[121], or complete
reflection[114], from the sample across a very narrow bandwidth. However, the main
limitation of metal-based Fano-resonant systems is the large non-radiative loss due to
Drude damping, which limits the achievable Q-factor[118] to less than ~10.
High-refractive-index dielectric particles offer a potential solution to the issue of
material (non-radiative) loss. For instance, dielectric Fano-resonant structures based on
oligomer antennae[46], silicon nanostripe[123], and asymmetric cut-wire
metamaterials[124], [125] have been demonstrated with Q-factors up to 127.
In this chapter, we describe the development of silicon (Si)-based metasurfaces
possessing sharp EIT-like resonances with a record high Q-factor of 483 in the near-
infrared regime. The high-Q resonance is accomplished by employing Fano-resonant unit
cells in which both radiative and non-radiative damping are minimized through coherent
interaction among the resonators combined with the reduction of absorption loss.
Combining the narrow resonance linewidth with strong near-field confinement, we
demonstrate an optical refractive index sensor with a figure of merit (FOM) of 103. In
addition, we demonstrate unit cell designs consisting of double-gap split-ring resonators
that possess narrow feed-gaps in which the electric field can be further enhanced in the
surrounding medium, allowing interaction with emitters such as quantum dots.
53
4.2 Design and Characterization
The schematic of the designed dielectric metasurface is shown in Fig. 4.1(a). The
structure is formed from a periodic lattice made of a rectangular bar resonator and a ring
resonator, both formed from Si. The rectangular bar resonator serves as an electric dipole
antenna which couples strongly to free space excitation with the incident E-field oriented
along the x-axis. The collective oscillations of the bar resonators form the “bright” mode
resonance. The ring supports a magnetic dipole mode wherein the electric field is directed
along the azimuthal direction, rotating around the ring’s axis. The magnetic dipole mode
in the ring cannot be directly excited by light at normal incidence as the magnetic arm of
the incident wave is perpendicular to the dipole axis; however, it can couple to the bright
mode bar resonator. Furthermore, the ring resonators interact through near-field coupling,
resulting in collective oscillation of the resonators and suppression of radiative loss,
forming the “dark” mode of the system. The interference between the collective bright
and dark modes form a typical 3-level Fano-resonant system[118], as illustrated in Fig.
4.1(b). The response of the dielectric metasurface is similar to the collective modes found
in asymmetric double-gap split-ring resonators in which the asymmetry in the rings yields
a finite electric dipole moment that can couple the out-of-plane magnetic dipole mode to
free space[126]–[131]. In our case, coupling to free space is provided by the bright mode
resonators which are placed in close proximity to the symmetric dark mode resonators.
Numerical simulations of the structure were carried out using a commercially-available
software (CST Microwave Studio) using the finite-element frequency-domain (FEFD)
solver. The simulated transmittance, reflectance and absorption spectra of the designed
structure are shown in Fig. 4.1(c), where a distinct EIT-like peak can be observed at a
54
wavelength of 1376 nm. In these simulations the resonators are sitting on a quartz
substrate and embedded in a medium with a refractive index of n = 1.44, matching the
experiments described below. We have also used the dielectric function of Si as
determined using ellipsometry and assumed an infinitely large array, resulting in a Q-
factor that reaches 1176, roughly 2 orders of magnitude higher than any previously
reported Fano-resonant plasmonic metamaterial[118]. Furthermore, the peak of the
transparency window approaches unity, demonstrating the potential to realize highly
dispersive, yet lossless, “slow light” devices.
Figure 4.1. (a) Diagram of the metasurface. The geometrical parameters are: = 150 nm,
= 720 nm, = 110 nm, = 225 nm, = 70 nm, = 80 nm, = 110nm, = 750 nm and = 750
nm. (b) Schematic of interference between the bright and dark mode resonators. (c)
Simulated transmittance (blue curve), reflectance (red curve), and absorption (green
curve) spectra of the metasurface. (d) Oblique scanning electron microscope image of the
fabricated metasurface. (e) Enlarged image of a single unit cell. (f) Experimentally
measured transmittance, reflectance, and absorption spectra of the metasurface.
55
The designed structure was fabricated by starting with a 110-nm-thick poly-
crystalline Si (refractive index =3.7) thin film deposited on a quartz (SiO2) ( =1.48)
wafer. The structure was patterned using electron beam lithography for mask formation
followed by reactive-ion etching. A SEM image of a fabricated sample is shown in Fig.
4.1(d),(e). Before optical measurements, the resonator array was immersed in a refractive
index matching oil ( =1.44) within a polydimethylsiloxane (PDMS) flow cell. (See
Methods for details). The experimentally measured transmittance, reflectance and
absorption spectra, plotted in Fig. 4.1(f), were acquired by illuminating the sample with
normal-incident white light with the electric field oriented along the long axis of the bar
resonator. A peak transmittance of 82% was observed at a wavelength of 1371 nm with a
Q-factor of 483, as determined by fitting the dark mode resonance to a Fano line shape
(see Appendix C1 for details). The shape of the measured spectra have good agreement
with the simulation, though the Q-factor and peak transmittance are reduced. This is most
likely due to imperfections within the fabricated sample which introduce scattering loss
and break coherence among the resonators. The role of coherence will be further
addressed below. Furthermore, additional loss in the Si arising from surface states created
during reactive ion etching leads to slightly increased absorption in the array compared to
theory. Nonetheless, this structure has the highest experimentally achieved Q-factor
among all plasmonic or dielectric optical metamaterials/metasurfaces reported to date. It
should also be noted that the use of index-matching oil is not needed to achieve such high
Q-factors.
n n
n
56
4.3 Theoretical Treatment
The response of the metasurface can be qualitatively understood by applying the
widely used coupled harmonic oscillator model[132], [133], described by the following
equations,
1 0 1 1 2 0
2 0 2 2 1
,
0,
j tx j j x j x gE e
x j j x j x
(4.1)
where and represent the amplitude of the collective modes supported by oscillators
1 (bright mode) and 2 (dark mode), respectively. and are the damping rates, given
by where and are the radiative and non-radiative decay rates,
respectively. is the central resonant frequency of oscillator 1, is the detuning of
resonance frequency of oscillator 1 and 2, and is the bright mode dipole coupling
strength to the incident electric field . is the coupling coefficient between oscillators
1 and 2 and given the close proximity of the resonators, it should be considered an
effective coupling coefficient that takes into account interaction between the bright mode
atom and its 2 nearest neighbors.
Of particular interest is the value of which reflects the damping of the
collective dark mode and plays a large role in dictating the linewidth of the EIT-like
resonance. The radiative damping term, 2R , is minimized due to the collective
oscillations of the array, mediated by near-field coupling between the unit cells. One
consequence of utilizing collective modes is that the value of 2R is inversely
proportional to the size of the array due to the fact that the discontinuity at the edges of
the array allows for light leakage to free space[134], [135]. While collective modes have
1x 2x
1 2
R NR R NR
0
g
0E
2
57
been utilized in past demonstrations of plasmonic EIT metamaterials to realize extremely
small 2R values, the Q-factors have intrinsically been limited by the Ohmic loss in the
metal. By replacing the resonator constituents with lossless dielectrics, the non-radiative
damping term 2NR can also be minimized, resulting in the large increase in the Q-factor
and peak transmittance.
Equally important is the role of the coupling coefficient, , in realizing a high Q-
factor resonance for this system. It has previously been shown that the slope of dispersion
is inversely proportional to . In the limit of , reduction of will result in a
monotonic increase of the Q-factor until is reached, at which point the Fano
resonance will vanish, leaving only the bright mode resonance. In our system, the
magnetic field from the bright mode resonator is inducing the dark mode resonance, as
illustrated in Fig. 4.2(a). Thus, as the spacing between the resonators ( 1g ) is increased the
coupling coefficient decreases, resulting in an increase in the Q-factor (Fig. 4.2c,d) and
strong magnetic and electric field localization (Fig. 4.2b). At a spacing of 1g = 74 nm, the
Q-factor reaches a value of ~30,000 which is indicative of the fact that both radiative and
non-radiative losses in the system are minimal, resulting in a situation wherein .
However, losses in the Si primarily arising from surface states created during etching will
ultimately limit the Q-factor, as has been demonstrated in microcavities[136]. Such losses
are not included in these calculations. It is also important to realize that the bright mode
resonator is also interacting with the dark mode resonator in the adjacent unit cell (D2),
inducing a magnetic field that is 180° out of phase with the excitation from the bright
mode resonator within its own unit cell. Therefore, when the gap between the bright
22 0
0
2 ~ 0
58
mode resonator and adjacent dark mode resonators are equal ( 1g = 75 nm, 2 1g g = 0)
the fields destructively interfere and goes to zero, resulting in elimination of the Fano
resonance, as can be observed in Fig. 4.2(b) and in the magnetic and electric field profiles
in Fig. 4.2(b).
Figure 4.2. (a) Schematic showing the coupling of the bright mode resonator to the
neighboring dark mode resonator. Here, we schematically provide the fields arising due
to the bright mode resonance. (b) Simulated magnetic and electric field amplitudes as a
function of resonator spacing. (c) Transmittance curve for the metasurface with varying
values of 1g obtained through FEFD simulation. 2 1g g is used to track the difference
in spacing between the bright mode resonator and the adjacent dark mode resonators. (d)
The extracted Q-factors of the EIT resonance as a function of .
59
Figure 4.3. (a) Vector plot of the magnetic field showing the coherent excitation of the
magnetic dipoles within the dark mode resonators. (b) Scanning electron microscope
images of the dielectric metasurface with different array sizes. The inset shows the
magnified view of a 20 by 20 array. (c) Transmittance spectra of arrays with different
sizes. d, The extracted Q-factors of the metasurface as a function of array size.
60
At the transmission peak the energy in the array is concentrated in the collective
dark mode with the magnetic dipoles in each of the split-rings oscillating coherently as
shown in Fig. 4.3(a). The array size thus becomes an important factor in the overall Q-
factor of the metasurface due to the fact that lattice perturbations at the array’s edge break
the coherence[134], [135], leading to strong scattering of light into free-space and
broadening of the resonance peak. To characterize this effect, we fabricated arrays of five
different sizes, consisting of 400 to 90,000 unit cells (SEM image of the test samples are
shown in Fig. 4.3b). In the measurement, we used a 5x objective for illumination and a
50x objective for collection with an aperture in the conjugate image plane on the
transmission side to confine the collection area to 15 μm x 15 µm. The measured spectra
are shown in Fig. 4.3(c) and we observe that the Q-factor increases with increasing array
size, saturating as we approach 90,000 unit cells. The saturation of the Q-factor indicates
the limit imposed by both incoherent radiative loss arising from inhomogeneities and
non-radiative loss arising due to finite absorption in the Si. As expected, the required unit
cell number needed to achieve spectral convergence is larger than that reported in
coherent plasmonic metamaterials due to the reduction in the non-radiative component.
Photonic crystal cavities possessing higher Q-factors have been reported[137],
though they lack the spatial homogeneity present in the metasurface outlined here.
Diffractive guided mode structures can also exhibit extremely high Q-factors[138],
though in our case we have the additional freedom of engineering the local field
enhancement through modification of the dark mode resonators. For instance, this can be
done by placing symmetric feed-gaps in the resonator forming a double-gap split-ring, as
shown in Fig. 4.4(a). In this case, the azimuthally oriented field located in the gap is
61
enhanced by a factor of (Fig. 4b), where and are the permittivities of the
resonator and surrounding medium, respectively. For the design depicted in Fig. 4.4, this
results in an electric field enhancement of 44 in the gap region. Having the advantages of
both a sharp spectral response and a strongly enhanced field in the surrounding substance
allows the metasurface to serve as an ideal platform for enhancing interaction with the
surrounding medium. To investigate the response of such structures, samples were made
using the same processes as described above and measured in n = 1.44 index matching oil.
An SEM image of the sample is shown in Fig. 4.4(c). The simulated and experimentally
measured transmittance curves are shown in Fig. 4.4(d) and result in theoretical and
experimentally measured Q-factors of 374 and 129, respectively. The lower theoretical
Q-factor, compared with the ring geometry, is due to the fact that the electric fields are
not equal the two arms of the split-ring due to the asymmetry of the unit cell. This results
in radiation loss to free space as the electric dipole moments do not fully cancel one
another. The decrease in the experimental Q-factor, compared to theory, is attributed to
more imperfections in the sample arising from the inclusion of the gaps, ultimately
resulting in increased scattering from the structure.
/d s d s
62
Figure 4.4. (a) Diagram of the metasurface. The geometrical parameters are: 2a = 150 nm,
2b = 600 nm, 2inr = 120 nm, 2outr = 250 nm, 3g
= 70 nm, 4g = 50 nm, = 110nm, 3p =
750 nm and 4p = 800 nm. (b) Simulated electric field amplitude distribution. (c)
Scanning electron microscope image of the fabricated metasurface. The inset shows a
single unit cell (scale bar of 200 nm). (d) Simulated (blue solid line) and measured (red
dashed line) transmittance spectrum of the metasurface.
4.4 Refractive Index Sensing
Due to their narrow linewidths, one interesting application of these metasurfaces
is optical sensing. Optically resonant sensors are characterized by both the linewidth of
the resonance ( ) as well as the shift in the resonance per refractive index unit change
( ). These two values comprise the FOM which is given by [139]. The
highest demonstrated FOMs for Fano-resonant localized surface plasmon resonance
(LSPR) sensors are on the order of 20[114], [140], [141]. Here, we examine the FOM of
the ring resonator metasurfaces and to further increase the sensitivity of our metasurface
to local index changes, we etched a 100-nm-tall quartz post below the Si resonators such
that the field overlap in the surrounding dielectric can be further promoted, as illustrated
in Fig. 4.5(a). The transmittance spectra of the metasurface when immersed in oil with
different refractive indices, from 1.40 to 1.44, are presented in Fig. 4.5(b), and it can be
seen that a substantial movement in the peak position is realized despite the small index
change. A linear fit of the shift in the resonance peak (Fig. 4.5c) leads to a sensitivity of
t
S FOM S
63
=289 nm RIU-1
, which is comparable, but slightly lower, than the best Fano-resonant
plasmonic sensors. The slight decrease in sensitivity is due to the fact that the index
contrast, and corresponding field enhancement, at the dielectric metasurface-oil interface
is still lower than that found in plasmonic structures. However, when combining the
sensitivity with an average resonance peak linewidth of only 2.8 nm, we arrive at an
FOM of 103, which far exceeds the current record for Fano-resonant LSPR sensors. With
further optimization of fabrication and more stringent control of the resonator coupling,
FOMs on the order of 1000 should be within reach.
Figure 4.5. (a) SEM image of the sample with the quartz substrate etched by 100 nm. (b)
Measured transmittance spectra of the EIT metasurface when immersed in oil with
refractive index ranging from 1.40 to 1.44. (c) The red circles show the experimentally
measured resonance peak position as a function of the background refractive index. The
blue curve is a linear fit to the measured data, which was used to determine the sensitivity
as 289 nm RIU-1
.
Furthermore, by introducing two feed-gaps in the dark mode ring resonator, we
can greatly enhance the local electric field intensity in the vicinity of the resonator, and
therefore increase the field overlap with the surrounding substance. Here, we also provide
the performance of the double-gap split-ring metasurface as a sensor (Fig. 4.7). To further
S
64
increase the sensitivity of our metasurface to local index changes, we again etched a 100-
nm-tall quartz post below the Si resonators, as illustrated in the SEM images in Figure
4.7(a). Compared with the ring-resonator metasurface, the double-gap split-ring sample
shows a greater sensitivity to local refractive index change due to the increased modal
overlap with the surrounding environment. By measuring the transmittance of the sample
in different index matching liquids and extracting the shift of EIT resonance peak, we
acquired a sensitivity S of 379 nm/RIU. However, when combining this with an average
experimentally measured resonance linewidth of 10.3 nm, we arrived at a sensing FOM
of 37, which is lower than the ring-resonator sample. The reason for the lower FOM is
obviously the broader resonance linewidth. As we have also stated in the main text, the
lower theoretical Q-factor, compared with the ring geometry, is due to the fact that the
electric fields are not equal in the two arms of the split-ring due to the asymmetry of the
unit cell. This results in radiation loss to free space as the electric dipole moments do not
fully cancel one another. The decrease in the experimental Q-factor, compared to theory,
is attributed to more imperfections in the sample arising from the inclusion of the gaps,
resulting in increased scattering from the structure.
65
Figure 4.6. (a) SEM image of the double-gap split-ring sample with the quartz substrate
etched by 100 nm. The inset is an enlarged image of a single unit cell (scale bar of 200
nm). (b) Measured transmittance spectra of the double-gap split-ring metasurface when
immersed in oil with refractive index ranging from 1.40 to 1.44. (c) The red circles show
the experimentally measured resonance peak position as a function of the background
refractive index. The blue curve is a linear fit to the measured data, which was used to
determine sensitivity of the structure as 379 nm/RIU.
4.5 Conclusion
In conclusion, dielectric metasurfaces can be used to significantly improve upon
the performance of their plasmonic counterparts in mimicking electromagnetically
induced transparency due to their greatly reduced absorption loss, resulting in sensing
FOMs that far exceed previously demonstrated LSPR sensors. With proper design, such
metasurfaces can also confine the optical field to nanoscale regions, opening the
possibility of using such metasurfaces for a wide range of applications including
bio/chemical sensing, enhancing emission rates, optical modulation, and low-loss slow
light devices.
66
Chapter 5 2D Dielectric Metasurface — Enhanced Nonlinearity
5.1 Introduction
Following Chapter 4, we further investigate the nonlinear optical properties of the
Fano-resonant Si metasurface. Nonlinear optics forms the basis for a number of useful
processes including light generation in parametric up- and down-conversion tunable
lasers[142], generation of entangled photons for quantum optics[150], and the nonlinear
Kerr effect for ultrafast all-optical light modulation[33], [143], [144]. However, the
nonlinear optical response of materials is intrinsically weak and thus a long interaction
length and / or high intensity is needed for efficient nonlinear light interaction. When
dealing with bulk crystals, the common method to boost nonlinear conversion is to
employ phase-matching between the fundamental and generated waves[142]. However,
phase matching still requires a relatively long sample interaction length which is
problematic for compact integrated devices.
A different approach is to employ resonance-induced electromagnetic field
enhancement. When employed in nanoscale films, this approach does not require phase
matching and takes advantage of the fact that the n-th order harmonic generation is
proportional to the integration of induced electric dipoles over the volume of a
nanostructure unit cell,
n
(n) (n) ,Vχ ω dV loc
p r E r (5.1)
where (n)χ is the intrinsic n-th order nonlinear susceptibility of the material, ,ω
locΕ r is
the local electric field, and V is the volume of a unit cell. As an example, localized
67
surface plasmon resonances can be utilized to substantially enhance the ,ωlocΕ r by
efficiently funneling light from the far-field to a deep sub-wavelength scale. However,
since the field maxima in plasmonic structures occurs at the boundary of the
metal/dielectric interface, the intrinsic nonlinearity of the metal cannot be efficiently
exploited. One way to mitigate this issue is to place nonlinear materials in the vicinity of
the plasmonic “hot-spots”[32], [151], [152]; however, the small modal volume of
plasmonic resonances will still limit the overall generation efficiency. Furthermore,
plasmonic nanostructures generally suffer from a low damage threshold due to large
optical absorption and the low melting temperature of metals compared to dielectrics. As
an alternative, low-loss dielectric structures (silicon nanodisks[153], for example)
exhibiting Mie resonances have recently been studied for enhancing third harmonic
generation (THG); however, achieving intense near-field enhancements, and therefore
high THG efficiencies, has remained challenging due to the leaky nature of the optical
modes[83], [84], [154]. On-chip photonic structures such as ring-resonators and slow
light waveguides have also been proposed for THG due to their ability to achieve large
quality factors (Q-factor) and / or long photon residence times[155], [156]. However, the
conversion efficiencies of such devices are limited due to two-photon absorption
(TPA)[149] of the fundamental wave within silicon (Si), a result of the long optical path
length of the bus waveguides.
In this chapter, we demonstrate a Fano-resonant[157], [158] Si-based metasurface
possessing large third-order nonlinearity for use in THG. The enhanced nonlinearity is
due to a high Q-factor Fano resonance that in turn strongly enhances the local electric
field within Si, thus resulting in large effective (3)χ . Unlike ring resonators and other chip-
68
based devices, there is no bus waveguide and thus TPA is greatly reduced while the
volumetric nature of the modes allows better overlap with the (3)χ material compared to
plasmonic implementations. This results in a metasurface with a THG enhancement of
more than 5 orders of magnitude and a conversion efficiency of on the order of 10-6
,
which is the highest value reported to date in micro or nanostructured films at comparable
pump energies[145], [159]. Furthermore, by combining the nonlinear Kerr effect with
the high Q-factor resonance, we experimentally demonstrate how the metasurface can be
used for all-optical modulation.
5.2 Linear Optical Properties
The Fano-resonant metasurface is illustrated in Fig. 5.1(a),(b) and consists of a
periodic lattice of coupled rectangular bar and disk resonators formed from Si. The
rectangular bar resonator supports a "bright" electric dipole resonance that is excited
when the incident electric field is along the x-axis. The disk supports a "dark" magnetic
dipole resonance in which the electric field is directed along the azimuthal direction,
rotating around the disk’s axis. The out-of-plane magnetic dipole in the disk cannot be
directly excited by normal incident light, but can instead be excited through near-field
interaction with the bright mode bar resonator. The interference between the collective
"bright" and "dark" modes forms a typical 3-level Fano-resonant system, as illustrated in
Fig. 5.1(c). The geometry of the nonlinear Si-based Fano-resonant metasurface is similar
to the linear one presented in Chapter 4. However, here we modified the “dark” mode
resonator from a ring- to disk-shape to further promote light interaction with the
nonlinear material (Si).
69
Polycrystalline silicon (Poly-Si) was chosen as the resonator material due to its
large linear refractive index (n~3.7) and large intrinsic third-order susceptibility and
nonlinear index ((3)
Siχ ~14 2 22.0 10 m V ,
2( )Sin ~18 2 12.7 10 m W ) in the near-infrared
band[163]. In order to fabricate the structures, a 120 nm thick poly-Si layer was first
deposited on a quartz substrate using low-pressure chemical vapor deposition (LPCVD).
The resonators were then defined using electron beam lithography (EBL) followed by
reactive-ion etching (RIE) (see Methods for further details). A scanning electron
microscope (SEM) image of the fabricated sample is shown in Fig. 5.1(d). The
experimentally measured transmittance, plotted in Fig. 5.1(e), was acquired by
illuminating the sample with normal-incident white light with the electric field oriented
along the long axis of the bar resonator. Numerical simulations of the structure were also
carried out using a commercially-available software (CST Microwave Studio) using the
finite-integration frequency-domain (FIFD) solver (see Methods for further details). A
sharp peak in the transmittance curve is observed at a wavelength of 1348 nm with an
experimental Q-factor of 466, as determined by fitting the dark mode resonance to a Fano
line shape. The measured spectrum line-shape agrees well with the simulation, though the
Q-factor and peak transmittance are reduced, which is expected due to imperfections with
the fabricated sample and additional material loss in the Si arising from surface states
created during RIE.
70
Figure 5.1. (a) Schematic of three photon up-conversion with the Fano-resonant silicon
metasurface. The blue bar resonators represent the “bright” mode, and the red disk
resonators represent the “dark” mode. (b) Diagram of one unit cell of the metasurface.
The geometrical parameters are: a = 200 nm, b = 700 nm, r = 210 nm, g = 60 nm, =
120nm, 1p
= 750 nm and2p = 750 nm. (c) Schematic of the Fano interference between
the bright and dark mode resonators. (d) An SEM image of the fabricated metasurface. (e)
Simulated (blue) and experimentally measured (red) transmittance spectra of the
metasurface.
5.3 Enhanced Third Harmonic Generation and Nonlinear Kerr Effect
Accompanying the narrow transmittance curve, the metasurface also possesses a
large electric field enhancement within the disk resonator, as shown in Fig. 5.2(a). The
field enhancement is on the same order as state-of-the-art nonlinear plasmonic
devices[32], [152]; however, in contrast to plasmonic structures, the field enhancement
occurs within the volume of the dark mode resonator with excellent modal overlap with
the (3)χ material (Si). The metasurface possesses the advantages of waveguide-based
devices such as a large Q-factor and good modal overlap with the active material while
t
71
greatly reducing parasitic losses such as TPA and direct THG absorption in the bus
waveguides.
In order to quantitatively determine the nonlinear enhancement, we first compare
the THG intensity from the metasurface with an un-patterned Si film with the same
thickness. In the THG intensity measurement, we use an optical parametric oscillator
(OPO) centered at 1350 nm as the pump, and focus the laser beam to a spot with an area
of ~225 um2 on the metasurface. The THG signal generated in the forward direction is
then collected by a high numerical aperture objective and sent to a grating spectrometer
with a liquid-nitrogen-cooled charge-coupled device (CCD) camera for spectroscopic
analysis (see Appendix D1 for details of the measurement set-up). The THG spectra of
the metasurface and un-patterned Si film are shown in Fig. 5.2b,c and demonstrate an
enhancement factor of 1.5×105. Further verifying the origin of the enhancement, the
metasurface shows no significant enhancement when illuminated with the electric field
orthogonal to the bar resonator, as is shown in Fig. 5.2b. By comparing the third
harmonic signal from a Si-on-quartz film and a bare quartz substrate (Fig. 5.2c), we
further excluded the effect of THG from the quartz substrate.
72
Figure 5.2. (a) Simulated electric field amplitude at the Fano resonance peak wavelength
of 1350 nm in both the x-y and y-z plane. The choice of cut-plane is represented with the
white dashed lines. (b) Third harmonic spectra of the metasurface with the incident
electric field polarized along x-axis and y-axis, respectively. (c) Third harmonic spectra
of an un-patterned Si film and a bare quartz substrate, respectively (average pump power
of 25 mW, peak pump intensity of 1.6 GW cm-2
).
In addition to THG enhancement, the strong near-field enhancement in the
metasurface can also substantially modify the refractive index of Si at the fundamental
wavelength via the nonlinear Kerr effect. This index change in turn shifts the Fano
resonance peak wavelength leading to all-optical modulation. Experimentally, this is
manifest in the third harmonic peak wavelength deviating from 0
/3 where 0
is the
linear Fano resonance peak. This is illustrated in Fig. 5.3a which demonstrates that the
THG peak deviates from the linear Fano resonance peak by 0.93 nm at peak pump
intensity of 0.8 GW cm-2
. Further increasing the pump intensity to 1.6 GW cm-2
results in
a 2.6 nm THG shift, demonstrating the expected intensity dependence. To better
understand the origin of the peak shifts, the index change of the Si ( n ) can be calculated
using:
73
2 2
0
2( ) 0SiV
Si
Si
E E dVn n I
V
(5.2)
where0I is the peak pump intensity,
2 2
0E E is the absolute field intensity enhancement
factor, and SiV is the volume of the Si resonator. As a first order approximation of the
magnitude of this effect, numerical simulations were used to calculate the field intensities
in the absence of any nonlinearities. Using equation 2, this yields a n of 0.0118 at 0.8
GW cm-2
peak pump intensity. Re-simulating the metasurface with the calculated n , we
find the Fano resonance peak shifts by 3.5 nm for the fundamental wave (corresponding
to a 1.17 nm THG shift), as is shown in Fig. 5.3b. While this is clearly a first order
approximation, the general trend in the resonance shift is readily reproduced.
Combining the nonlinear Kerr effect with the narrow bandwidth of the linear
transmittance spectrum, The Fano-resonant Si metasurface can serve as an ultra-thin all-
optical modulator. In particular, we show the modulation of transmittance upon
increasing the pump power in Fig. 5.3c. At 1348 nm (the linear Fano resonance peak), the
transmittance gradually decreases with increasing pump power due to the fact that the
Fano resonance peak red-shifts away from the pump wavelength. At 1352 nm, the
transmittance shows a peak at ~1.6 GW cm-2
pump power as we pass through the
resonance and gradually decreases as the resonance peak moves to 1352 nm with
increasing pump power. At a pump wavelength of 1356 nm we begin considerably blue-
shifted from the resonance and upon increasing pump power the transmittance shows a
maximum at ~1.8 GW cm-2
resulting in a modulation depth 0 0T T T of 36%, where 0T
is the linear transmittance of the sample. In these measurements, we focus the laser to a
tight spot of ~225 um2, which introduces a finite angle of incidence. As the Fano
74
resonance is relatively sensitive to the incident angle (see Appendix D2 for details), the
contrast in transmittance is lower when compared with the measured linear transmittance
spectra in which near-normal incidence white light is utilized.
Figure 5.3. (a) The wavelength-dependent THG intensity of the metasurface when
normalized to an un-patterned Si film of the same thickness. The blue points are data
taken under 0.8 GW cm-2
peak pump intensity, and the red points are data taken under 1.6
GW cm-2
peak pump intensity. The black dash line indicates the linear Fano resonance
peak. (b) Simulated transmittance of the metasurface under different pump intensity. The
measured transmittance under low power white light illumination is also shown as the
black dashed line for a reference. (c) The relative change in transmittance as a function of
pump power at 1348 nm, 1352 nm and 1356 nm. The black dash line shows the shift of
the transmittance peak with increasing pump power.
75
5.4 Absolute Third Harmonic Efficiency
The absolute THG efficiency for the Fano-resonant Si-based metasurface was
characterized by simultaneously measuring the pump and THG beam power (see
Appendix D1 for details of the measurement). Based on these measurements, a
conversion efficiency of 1.18×10-6
with an average pump power of 50 mW and a peak
pump intensity of 3.2 GW cm-2
was measured, as shown in Fig. 5.4a. These
measurements were performed with a pump laser with a linewidth of ~15 nm, which is
much greater than the linewidth of the Fano resonance (~2.9 nm). A photograph of the
sample under 50 mW average pump power (Fig. 5.4b) clearly shows the third harmonic
blue light emission. However, to achieve higher conversion efficiency and reach the
saturation threshold of the metasurface, a pump laser with larger peak intensity is
required. To achieve this, we used the signal output of an optical parametric amplifier
(OPA) as the pump and repeated the absolute THG efficiency measurement (see
Appendix D1 for details of the measurement). With an OPA as the pump, we measured a
conversion efficiency of 7.2×10-6
with a plateau in the conversion efficiency occurring at
300 GW cm-2
. The relatively low conversion efficiency at the large pump fluence is most
likely due to the Fourier-transform-limited bandwidth of the OPA signal (~60 nm).
Namely, the large bandwidth of the laser results in inefficient coupling of the pump beam
to the resonant mode of the metasurface, which has a linewidth of only ~2.9 nm. To
further increase the conversion efficiency, a chirped pulse with the maximum of the pulse
centered at the Fano resonance peak wavelength could be used. Nevertheless, the THG
saturation intensity demonstrated here is still orders of magnitude higher than previously
76
reported nanoscale nonlinear photonic devices[145], [159]. While the THG of many on-
chip nonlinear photonic devices such as ring resonators and slow-light waveguides[155],
[156] suffer from saturation due to TPA of the fundamental wave, here the THG is only
moderately affected by TPA due to the sub-wavelength thickness of the metasurface.
Figure 5.4. (a) Log-log plot of the third harmonic power as a function of the pump power
and the peak pump intensity with OPO. The red circles indicate the measured data, and
the blue line is a numerical fit to the data with a third-order power function. The green
circle denotes the pump power at which the photograph in panel b was taken. The inset
shows the extracted absolute THG efficiency as a function of the pump power. (b) A
photograph taken under ambient room light showing blue light emission from the sample
for an incident wavelength at 1350 nm (average pump power of 50 mW, peak pump
intensity of 3.2 GW cm-2
). (c) Log-log plot of the third harmonic power as a function of
the pump power and the peak pump intensity with OPA. The inset shows the extracted
absolute THG efficiency as a function of the pump power.
5.5 Conclusion
To summarize, utilizing the large near-field enhancements in a Fano-resonant Si-
based metasurface, we have demonstrated highly efficient visible (blue) THG and all-
optical nonlinear modulation. Such a platform can also be applied for other nonlinear
processes such as four-wave mixing[34], Raman amplification[164], and may even be
extended to Si-based coherent lasing[165]. By combining the Kerr shift with the narrow
77
bandwidth of the linear transmittance spectrum the dielectric metasurface potentially
opens a new route towards the realization of ultra-compact optical devices such as
saturable absorbers and modulators.
78
Chapter 6 Metamaterial Perfect Absorber-based Quantum Well Infrared
Photodetector
6.1 Introduction
Metamaterials have been demonstrated as an extremely versatile platform for
controlling light matter interaction, showing capability in manipulating light emission,
light propagation and light detection, as illustrated in the previous chapters of this
dissertation. However, most metamaterials and metasurfaces to date are passive/quasi-
passive devices. There has been a constant drive in the metamaterial research community
to integrate metamaterials with active materials which change properties upon external
stimuli in order to realize dynamically switchable meta-devices.
When high speed switching is not the prime objective, metamaterials can be tuned
using microelectromechanical (MEMS) actuators that reposition parts of the
metamolecules, along with other candidates such as chalcogenide glasses and liquid
crystals [166]. To achieve high speed operation, people have already demonstrated
dynamic tuning of a metamataerial’s response at terahertz frequency by injection or
optical generation of free carriers in a gallium arsenide or silicon substrate[167]. “Phase-
change” materials are also promising for fast optical switching. In particular, the metal-
insulator phase transition of vanadium dioxide can lead to a dramatic change in the
dielectric and plasmonic properties[168]. Recently, it has also been found that a
substantial change in the dielectric properties of a nanometer-thick layer can be achieved
in conducting oxides through the injection of free carriers. By utilizing the inter- and
intra-band transition, one can also achieve large modulation of the dielectric function of
79
graphene, in particular at IR and terahertz frequencies[169]. Combining such active
materials with metamaterials, one can manipulate the resonant transmission or absorption
of a hybrid meta-device, and therefore realizing controllable light propagation or
detection. Other than the options listed above, scientists have recently found that
metamaterials can interact with intersubband transitions in semiconductor quantum wells
(QWs) such that a hybrid device with dynamic response tunability can be
manufactured[170]–[172].
In this chapter, we focus on how one can integrate metamaterials with the active
QWs to achieve enhanced photodetection in the long-wave infrared band ( 10λ μm ).
Here, we design a quantum well infrared photodetector (QWIP) that possesses near-unity
absorption for normal-incident mid-infrared light. The perfect absorption is achieved by
spectrally overlapping the magnetic-dipole resonances of a patterned dielectric QW stack
with the electric-dipole resonances of patterned metallic strips to achieve impedance
matching to free space at the frequency of the intersubband dipole transition of the
quantum well. This dielectric and metal hybrid structure utilizes a surface plasmon
resonance in the metallic strips to further promote light confinement within the QW as
otherwise light tends to leak out into the high index substrate. The near-unity optical
absorption in the active region of the QW, when combined with efficient photon-carrier
generation and transport, can lead to greatly boosted photo-responsivity of the QWIP.
80
Figure 6.1. (a) An SEM image of a thermally controlled reconfigurable photonic
metamaterial[166]. (b) Experimental design of an active THz metamaterial device based
on carrier injection into the GaAs substrate[167]. (c) Hybrid split-ring resonator
metamaterials based on vanadium dioxide[168]. (d) Schematic rendering of a gate-
controlled active graphene metamaterial composed of a SLG deposited on a layer of
hexagonal metallic meta-atoms[169].
6.2 Background
6.2.1 Intersubband Transitions & Quantum Well Infrared Photodetectors
For conventional photodetectors interband optical absorption is utilized and
corresponds to photo-excited carriers transiting across the band gap Eg (Fig. 6.2a). In a
detector structure these generated photocarriers can be collected through an external bias
or a p-n junction, thereby producing a photocurrent. By controlling the Eg, the spectrum
of the absorption and hence the wavelength dependence of the detector response can be
modified. In the long-wavelength infrared region where 10λ μm , the required band gap
81
is 0.1gE eV . Small-band-gap materials, such as mercury cadmium telluride (MCT), can
manufactured, but are also more difficult to grow, process, and fabricate compared to
larger-band-gap semiconductors[173]. To overcome this issue, the use of intersubband
(intraband) transition involving the transition within the same band has been proposed. In
order to create these subbands, QWs are used.
The QW is typically formed from narrow band-gap semiconductors (such as
gallium arsenide, GaAs) sandwiched between two layers of a material with wider band-
gap (such as aluminum gallium arsenide, AlGaAs), as is shown in Fig. 6.2(b). Such a
structure can be grown by molecular beam epitaxy (MBE) or metal-organic chemical
vapor deposition (MOCVD) with precise thickness control down to an atomic layer. The
solution to the band structure of a QW is similar to the well-known “particle in a box”
problem in quantum mechanics, which can be solved by the time-dependent Schrodinger
equation. The solved eigen-values determine the allowed states of the particle. As an
approximation, for the infinitely-high barriers and parabolic bands, the energy levels in
the QW are given by,
2 2
2
* 22j
w
πE j
m L
(6.1)
where wL is the width of the well,*m is the effective mass of the carrier in the quantum
well, and j is an integer. Therefore, the intersubband energy between the ground and the
first excited state is,
2 2
2 1 * 2
3
2 w
πE E
m L (6.2)
A typical QWIP utilizes the photo-excitation of the electron between the ground
82
and the first excited state ( 1 2E E in Fig. 6.2b). However, in order to create these states
within the conduction band these QWs must be doped becauseghν E and thus the
incident photon energy is not sufficient to create photocarriers.
The growth of semiconductor QWs is relatively mature and is low-cost. In
addition, the quantum well parameters can be designed to vary the intersubband optical
spectrum at will whereas the band-gap of a typical semiconductor photodetector utilizing
interband transition is fixed
Figure 6.2. (a) Band diagram of interband transition occurring in a conventional intrinsic
infrared photodetector. (b) Band structure of a QW. Intersubband transition between
electron levels E1 and E2 is schematically shown.
.
6.2.2 Optical Coupling Method for Quantum Well Infrared Photodetectors
One major challenge associated with using QWs for infrared photodetection is
that QWIPs do not absorb normal incident light because the light polarization must have
an electric field component normal to the growth direction of the well to be absorbed by
the confined carriers. When the incoming light contains no polarization element along the
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growth direction the matrix element of the interaction vanishes. As a consequence, an
alternative light coupling scheme is required.
Figure 6.3. (a) Conventional 45 degree wedge waveguide coupling. (b) Schematic
diagram of 2-D periodic gratings. (c) Layer diagram of a four-band QWIP device and the
deep groove periodic grating structure. Figure adapted from ref.[174].
The most commonly adapted approach is to illuminate the QWIP through a 45°
polished facet[174]. However, this illumination scheme limits the configuration of
detectors to linear arrays and single elements. For applications such as imaging, it is
necessary to couple light uniformly to a two-dimensional (2D) array of these detectors.
Alternatively, several monolithic grating structures such as linear and 2D periodic
gratings have been proposed and demonstrated for efficient light coupling to QWIPs and
to enable QWIP-based imaging. These gratings deflect the incoming light away from the
direction normal to the surface and scatter light into orders with a parallel wave-vector
that is an integer multiple of the reciprocal lattice-vector of the gratings. However, the
diffraction efficiency and thus the absorption in the QW region is typically less than
10%[175].
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6.3 Design of a Metamaterial Perfect Absorber with Integrated Quantum Wells
6.3.1 One-dimensional Polarization-sensitive Design
Figure 6.4. 3D view of the quantum well-integrated metamaterial perfect absorber. The
top and bottom Au layers have a thickness of 50 nm. The other geometric parameters are
p=3500 nm, a=1500 nm, t=1000 nm.
To start, we first examine a 1D perfect absorber design which is sensitive to the
polarization of the incoming light. The device schematic of the quantum well-integrated
metamaterial perfect absorber is shown in Fig. 6.4 The structure is composed of a top Au
layer, a top n-doped GaAs contact layer, an active QW layer, a bottom Au layer and a
bottom n-doped GaAs contact layer sitting on an intrinsic GaAs substrate.
85
Figure 6.5. The real and imaginary permittivity of the GaAs quantum well along the z-
(quantum well growth)-direction.
In order to calculate the optical response of the QW-integrated metamaterial
perfect absorber, the frequency dependent permittivity tensor of the composite materials
needs to be obtained. The gold permittivity is described using a Drude model with an
angular plasma frequency of 122 2060 10 rad/s and a damping rate of
122 10.9 10
1/s. By only considering the transition between the two lowest subbands, the permittivity
tensor for a gallium GaAs/AlGaAs quantum well grown in the [001] direction is,
0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 1
b
GaAs
QW b
GaAs GaAs
b
GaAs
(6.3)
where
2221
0
0 21 21 2
zNe
i
(6.4)
where 10.7b
GaAs is the permittivity of bulk GaAs crystal, N=181.2 10 1/cm
3 is the
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electron doping density, 21 0.67z is the dipole strength, 21 30 THz is the dipole
transition energy, and 21 3 THz is the damping rate. The real and imaginary part of Z
of the QW are plotted in Fig. 6.5. Note that the intersubband transition only occurs along
the quantum well growth direction, which leads to a strongly anisotropic behavior of the
effective QW permittivity.
Figure 6.6. Transmission, reflection and absorption spectra of the structure from full
wave simulation under normal plane wave illumination.
When the structure is illuminated with electric field along the x-direction,
localized surface plasmon resonance (electric dipole resonance) can be excited at both the
top and the bottom Au layer with anti-parallel current flow, as can be observed in Fig.
6.7(a). In addition, a magnetic dipole resonance, similar to the one in the zero index
metamaterial, is excited in the cavity formed in the dielectric QW layer, as is shown in
Fig. 6.7(b). By carefully designing the resonator length a, quantum well height t, and the
87
periodicity p, the electric and magnetic dipole resonances can be spectrally overlapped,
leading to near-unity absorption as calculated using full-wave simulation and shown in
Fig. 6.6. The full-width-at-half-maximum (FWHM) of the absorption peak is 5.5 THz,
well beyond the FWHM of the intersubband transition. Furthermore, we calculated the
power loss density of the structure at 30 THz, and find that over 95% of the light
absorption occurs in the active QW layer. This architecture also enables one-step
lithography, dry-etching and metal evaporation, greatly simplifying the conventional
metamaterial perfect absorber fabrication, which typically requires a separate step for
defining the bottom Au reflector. This is especially important because that the active QW
layer can only be epitaxially grown on a GaAs substrate and cannot be growth directly on
an Au backplane.
Figure 6.7. (a) Vector plot of the electric field from full wave simulation with the
frequency of incident light at 30 THz. (b) Simulated magnetic and electric field
amplitudes with the frequency of incident light at 30 THz.
6.3.2 Device Performance Versus Incident Angle
Another important metric of a photodetector is the light acceptance angle. In
88
contrast to previously demonstrated metal grating-based quantum well infrared
photodetectors that utilize the excitation of non-localized propagation surface plasmon
modes through grating coupling, our structure relies on spectrally overlapping the
magnetic-dipole Mie resonances of a patterned QW stack with the localized surface
plasmon resonances of patterned gold strips, therefore preserving a relatively angle-
insensitive response.
It can be seen from Fig. 6.8(a) that for transverse electric- (TE-) polarized light
where the electric-field is always parallel to the QW surface; the absorption is maintained
above 80% for incident angles up to 60°. For transverse magnetic- (TM-) polarized light,
the structure is more sensitive to the incident angle, as is shown in Fig. 6.8(b). This
originates from the anisotropic absorption of the QWs.
Figure 6.8. The simulated angular dispersions of the absorbance peak for TE(a) and TM
configurations(b).
89
6.3.3 Two-dimensional Polarization-Insensitive Design
In order to achieve a polarization-independent photo-response, the 1D stripe
resonators can be replaced by square resonators. However, to ensure electrical connection
on the top side, thin-metallic bus-bars are also needed. The schematic of the polarization-
independent design is shown in Fig. 6.9(a). The polarization-independent perfect absorber
structures still maintain a near-unity absorption, as is illustrated in Fig. 6.9(b).
Figure 6.9. (a) 3D view of the quantum well-integrated metamaterial perfect absorber.
The top and bottom Au layers have a thickness of 50 nm. The other geometric parameters
are p=3500 nm, a=1500 nm, t=1800 nm, w=400 nm. (b) Simulated absorption spectra of
the structure under normal plane wave illumination with electric field polarized along x-
direction (blue) and y-direction (red), respectively.
6.3.4 Routes Towards Device Fabrication and Characterization
While the fabrication and testing of the structure is beyond the scope of this
dissertation, the routes towards the experimental realization of the metamaterial perfect
absorber-integrated QWIP are still presented here. The quantum well stack, including an
n-doped GaAs conduction layer (bottom electrode), AlGaAs multiple quantum wells and
90
an n-doped GaAs buffer layer, can be grown using molecular beam epitaxy (MBE). The
perfect absorber structure can be created through the combination of electron/photo-
lithography, reactive-ion etching of the multiple quantum well stack, and metal
deposition. The top electrical contact can be achieved through direct contact with the top
metal film, while the bottom contact can be defined on top of the exposed n-doped GaAs
conduction layer beneath the active QW layer. Both polarization-sensitive and insensitive
devices can be fabricated as well as a multiple-pixel detector composed of perfect
absorber-based device elements resonant at multiple wavelengths.
The optical absorption spectrum can be measured using a Fourier-transform
infrared spectroscopy (FTIR) microscope system and the photo-responsivity,
photocurrent spectrum, and dark current noise of the device can be measured using a
tunable CO2 laser as a light source.
6.4 Conclusion
This device architecture overcomes the issue of low photo-responsivity in
conventional quantum well infrared photodetectors due to inefficient coupling and
absorption of normal incident light. The designed quantum well infrared photodetector
structure supports a perfect absorber-type resonant mode. The resonant mode has a large
out-of-plane electric field component, overlapping with the out-of-plane dipole transition
of the quantum well, allowing near-unity absorption in the active quantum well layer and
therefore high photo-responsivity.
Compared to the current techniques of using a 45 degree wedge waveguide or
periodic metallic gratings and roughened random reflectors, our approach preserves a
91
greatly boosted photo-responsivity and compact device architecture. Polarization-
insensitive photodetection can also be realized through a two-dimensional perfect
absorber design with a thin electrical bus-bar. With a pixelated perfect absorber design
with different absorber geometries and intersubband transition frequencies, we envision
multi-color and/or broadband photodetection can be realized.
92
Chapter 7 Conclusion and Outlook
The focus of this research has been to engineer the resonance properties of
dielectric metamaterials and metasurfaces for a variety of applications including
enhanced light emission, polarization and phase manipulation, bio-sensing, enhanced
nonlinear interaction, and enhanced infrared photodetection. There were several
impactful results obtained on this journey of probing the exotic behavior of resonant
dielectrics. In this chapter, I will summarize these findings as well as outline several
promising research directions in the metamaterial field.
7.1 Conclusion
In Chapter 2, I described the first experimental realization of an impedance-
matched low-loss 3D zero-index metamaterial (ZIM) with all-dielectric components at
optical frequency. A metamaterial exhibiting an effective refractive index of zero was
designed and fabricated based on low-loss silicon (Si) resonators. The ZIM has a nearly
isotropic response for transverse magnetic polarized light, which leads to its angular
selectivity and the ability to enhance and direct the spontaneous emission of the
embedded quantum dot emitters within the ZIM.
In Chapter 3, I transitioned the focus from bulk 3D dielectric metamaterials to the
study of ultrathin 2D dielectric metasurfaces. I showed that engineered dielectric nano-
antennas exhibiting Mie resonances can be used in place of plasmonic antennas to
drastically modify the phase of light while maintaining near-unity efficiency. I
experimentally demonstrated highly efficient linear polarization conversion with more
93
than 98% conversion efficiency over a 200 nm bandwidth in the short-wavelength
infrared band. In addition, I demonstrated optical vortex beam generation using a silicon-
based meta-reflectarray with azimuthally varied phase profile.
In Chapter 4, I studied of the dielectric metasurface analogue of
electromagnetically induced transparency. Due to extremely low absorption loss and
coherent interaction of neighboring meta-atoms, I realized Fano-type resonances with
quality factors of 483. This is realized by forming a periodic array of coupled electric and
magnetic dipole antennas and the associated minimization of the non-radiative decay of
light. Combining the sharp resonance with strong field confinement in its surrounding
medium, I show that such a device can be an ideal platform for bio-sensing, and
experimentally demonstrated a refractive index sensor with a figure-of-merit of 103.
In Chapter 5, I further investigated nonlinear light-matter interaction in Fano-
resonant dielectric metasurfaces. The metasurface results in strong near-field
enhancement within the volume of the silicon resonator while minimizing two photon
absorption, leading to greatly enhanced efficiency and increased saturation power for
third harmonic generation. The enhanced nonlinearity, combined with a sharp linear
transmittance spectrum, results in transmission modulation via the Kerr effect with a
large modulation depth.
In Chapter 6, I presented a design for a quantum well infrared photodetector
integrated with the concept of metamaterial perfect absorbers. By stringently overlapping
the electric and magnetic resonances of a quantum well-metal hybrid, the structure can
achieve near-unity light absorption in the quantum wells, leading to greatly enhanced
quantum efficiency of a quantum well-based infrared photodetector. A practical
94
fabrication and optical/electrical characterization schematic has also been outlined.
7.2 Future Outlook of Metamaterials
During the past two decades, researchers have used metamaterials to obtain
numerous unique optical properties not attainable from conventional optical components.
However, a greater challenge remains regarding the realization of practical meta-
“devices” with superior performance. Beyond reducing material loss, as outlined in this
thesis, I believe there are many other attractive directions to pursue. Here I briefly list a
few.
The first area of interest, I believe, is compact electrically-tunable 2D
metasurfaces. Although active metamaterials allowing dynamic modulation of light flow
have been one of the major directions in the metamaterial research community for many
years, there are still significant issues such as the realization of low-voltage electrical
modulation in a compact platform and the realization of “on/off”-style tuning instead of
only minor spectral modification. To achieve low-voltage electrical modulation, the
utilization of tunable intersubband transitions in quantum wells can be particularly
interesting, as it allows dramatic modulation of the dipole transition energy with a low
voltage bias when the quantum wells are asymmetrically coupled. To realize the
“on/off”-style modulation, a better engineered far-field spectral response and near-field
interaction of the optical field and the active material needs to be achieved.
Another interesting topic is to integrate the design concept of metamaterials with
gain materials for greatly reducing the lasing threshold of solid state semiconductor
lasers. I believe there is much to explore here as metamaterials may offer the ultimate
95
design freedom for engineering the Purcell factor and the local environment for emitters.
Finally, I believe another interesting route is to use metamaterials to enhance the
performance of existing optoelectronic devices such as waveguides, CMOS imaging
sensors, and photovoltaics, in which case a much more comprehensive evaluation
involving the performance gain, system robustness, and cost has to be conducted.
96
Appendix A: Zero-index Metamaterial
A.1 Retrieval of the effective index from the Bloch modes
Retrieval of the permittivity and permeability was carried out by extracting the
average field components from the TM Bloch modes at the boundary of the unit
cell (�̅�𝑥, �̅�𝑥, �̅�𝑦, �̅�𝑦, �̅�𝑧, �̅�𝑧). In the extraction of the permittivity and permeability, we
ensure the continuity of the tangential and normal components of the average field at the
unit cell boundary, ensuring that Maxwell’s equations are satisfied. The constitutive
equations for the average fields are then given by,
[
�̅�𝑥�̅�𝑦
�̅�𝑧
] [
𝜀0 ∗ 𝜀𝑥 𝐴𝑥𝑦 𝐴𝑥𝑧𝐴𝑦𝑥 𝜇0 ∗ 𝜇𝑦 𝐴𝑦𝑧𝐴𝑧𝑥 𝐴𝑧𝑦 𝜇0 ∗ 𝜇𝑧
] [
�̅�𝑥�̅�𝑦
�̅�𝑧
] (A.1)
The diagonal elements of the 3 x 3 parameter tensor define the permittivity (𝜀𝑥 )
and permeability (𝜇𝑦, 𝜇𝑧) of the bulk structure along the x, y and z directions respectively.
A.2 Optical property retrieval from the Bloch modes and extended states
To ensure that an accurate retrieval of the material properties was acquired, we
compared the retrieved wavevector, computed with the retrieved effective index, to the
band structure calculated numerically using MIT Photonic Bands (MPB) in the range
from Γ to Х, as illustrated in Fig. A.1(a). The retrieved band structure has a very good
agreement with the MPB band structure at smaller 𝑦, though it deviates at large 𝑦 as
spatial dispersion becomes apparent near the band edge. Only the transverse bands are
considered in the calculation of the effective optical properties.
In order to properly assign a refractive index to a material for off-normal angles of
97
incidence, there must be only one propagating band at a particular frequency. To verify
that there is only one propagating band within the material, we simulated the extended
states of the crystal, shown in Fig. A.1(b). Within the frequency range from 215 THz to
225 THz, slightly above the zero-index point, there is a single band (TM4) throughout k-
space. Within this region, a refractive index may be assigned to the metamaterial, though
it may change slightly with the angle of incidence, as illustrated in the IFC plot shown in
Fig. 2.2(d).
Figure A.1. (a) The solid lines represent the band structure of the square lattice
calculated from MPB and the circles correspond to band diagram retrieved from effective
index and the dispersion relation 𝑦 ⁄ . The mismatch of the two methods
at the band edge is due to the fact that the effective medium approximation no longer
holds in those regions. (b) Extended states of the crystal showing that only one band
(TM4) is present between 215 THz and 225 THz, allowing an effective index to be
assigned to this region.
A.3 Optical property retrieval from the Bloch modes and extended states
To further justify our claim that the proposed metamaterial structure can indeed be
homogenized as an effective medium and has an isotropic low index property for TM-
polarized light, we conducted numerical simulation with a Gaussian beam incident at the
ZIM from multiple angles. The wavelengths of the incident beams (1340nm and 1380nm)
98
are chosen such that they fall within the bandwidth where only one propagating band
(TM4) exists.
The simulated electric field profiles with multiple angles of incidence and
wavelengths are shown in Figs. A.2 (a)-(f). In all cases, we see no higher order diffraction
taking place at the exit surface of the sample. The transmitted light from the material is
plane wave like as shown in Figs. A.2 (a),(b),(d),(e) for normal and low angle incidence,
while light transmission is clearly forbidden at even higher angles of incidence due to the
conservation of parallel angular momentum (Figs. A.2c,f).
From the field plots in Fig. A.2(b), with 10° incidence at 1340 nm, the light
refracts at an angle of ~ 43° with clearly longer effective wavelength inside the material.
From simple calculation from Snell’s law we find the corresponding neff agrees well with
retrieved index of 0.254. The same phenomenon occurs with 5° incidence at 1380 nm
where the refraction angle is ~ 46°, which corresponds to a neff of 0.121 and again
matches our parameter retrieval result.
In Figs. A.2(g)-(i), we illustrated the refraction phenomenon at 1458 nm which is
negative index region where calculated index is -0.121, i.e. the same absolute value of
index for 1380 nm wavelength. With 0° angle of incidence the light transmits normally
out of the material with plane wave profile. With 5° incidence we can clearly see the
negative phase propagation inside the medium, finally light transmitting out of the exit
surface at 5° from the normal. But contrary to the refraction phenomenon at 1380 nm,
refraction is not forbidden at 30º angle of incidence for 1458 nm wavelength, due to
coupling to the longitudinal band at higher angle.
99
Figure A.2. (a)-(c), Light incidence at 0°, 10°, 30° respectively at wavelength of 1340
nm. (d)-(f), Light incidence at 0°, 5°, 20° respectively at wavelength of 1380 nm. (g)-(i),
Light incidence at 0°, 5°, 20° respectively at wavelength of 1458 nm.
100
Appendix B: Meta-reflectarray
B.1 Fabrication of Meta-reflectarray
Amorphous silicon (Si) (n=3.7) was chosen as the resonator material due to its
high index contrast. In order to incorporate the silver mirror while also using LPCVD for
the Si layer, we reversed the conventional fabrication steps by first depositing silicon on
quartz, followed by patterning the cut-wires and addition of the low index spacer and
silver mirror. Amorphous Si was deposited on quartz using an LPCVD horizontal tube
furnace. A quartz caged boat was used to contain the wafer to improve cross wafer
uniformity. Deposition temperature was 550 °C and process pressure was 300 mTorr.
Process gases were introduced into the tube furnace via mass flow controllers by flowing
50sccm’s of 100% SiH4.
The silicon cut-wire patterns were created by a sequential process of EBL, mask
deposition, lift-off and RIE. In the EBL process, we coated a 10 nm chrome charge
dissipation layer on top of PMMA resist to avoid surface charging, and the chrome layer
was subject to chemical removal prior to the resist development. The total pattern size
was ~1 mm x 1 mm for the polarization converter and 3 mm x 3 mm for the vortex beam
generator, both patterns were written using a JEOL 9300FS 100kV EBL tool. We used a
fluorine-based RIE recipe to etch the silicon with 80 W RF, 1200 W ICP power and C4F8,
SF6, O2 and Ar gas flows.
PMMA was then spin-coated on the sample, followed by soft baking (180 degrees
for 2 minutes) and reflowing at 300˚ C for 2 minutes to reach the desired thickness and
flatness. In the last step, 150 nm of silver was thermally deposited on top of the sample,
101
serving as the ground plane mirror. The entire process is summarized in Figure B.1.
Figure B.1. (a) LPCVD silicon on quartz. (b) EBL patterning. (c) Etch mask deposition
and lift-off. (d) RIE. (e) PMMA spinning and silver deposition.
B.2 Device Performance with Changing Incident Angle
Here we provide the angle-dependent response of the meta-reflectarray for both s-
and p-polarized light as is shown in Fig. B.2. From the result, we find two interesting
features. First of all, the bandwidth of the highly efficient polarization conversion gets
102
reduced with increased angle of incidence. More interestingly, extremely high Q-factor
guided mode resonance can be excited. This phenomenon has been well explained in
theory as the Fano-type interference of free space light and photonic crystal mode[138],
and has been experimentally observed previously[176]. We agree with the reviewer that
this may be a limiting factor for the waveplate operation in reflection mode. However, the
extremely high Q resonant mode may open up new avenues for application such as
sensing and enhanced light emission in cross-polarized or circularly polarized mode,
which can be potentially very interesting.
Figure B.2. Cross-polarization reflectance as a function of incident angles for (a) s- and
(b) p-polarized light respectively.
103
Appendix C: Dielectric Metasurface Analogue of Electromagnetically Induced
Transparency
C.1 Q-factor Extraction
We used a Fano model to extract the Q-factor of the EIT resonance from the
dielectric metasurface. The experimentally measured transmittance expT was fitted to a
Fano line shape given by
2
1 2
0
Fano
bT a ja
j
, where 1a , 2a and b are constant
real numbers; 0 is the central resonant frequency; is the overall damping rate of the
resonance. The experimental Q-factor was then determined by0
2Q
. The fit was
performed over the wavelength range from 1367 nm to 1380 nm as this model only
encompasses the Fano line shape and does not include the fit to the background
resonance provided by the bright mode. We used a fitting method identical to the one
used in a recent demonstration of silicon-based chiral metasurface25
, therefore rendering
the reported Q-factors in both cases comparable. The fit is shown in Fig. C.1
104
Figure C.1. Fano fit of the experimentally measured transmittance spectrum.
105
Appendix D: Nonlinear Dielectric Fano-resonant Metasurface
D.1 Measurement Set-up
D.1.1 Linear/Nonlinear Spectroscopy
The linear transmittance of the metasurface was measured using a custom-built
free-space infrared microscope. A tungsten/halogen lamp was used as the light source and
the metasurface array with a size of 300 μm x 300 μm was imaged using an infrared
camera. To restrict the angle of incidence to near-normal, a low numerical aperture (NA)
objective (Mitutoyo, 5x, 0.14 NA) was used to weakly focus the light on the metasurface,
with the NA further cut down to 0.025 by an aperture at its back focal plane. The
transmitted light was then collected by a high NA objective (Nikon Plan Apo Lambda,
60x, 0.95 NA) and coupled to an InGaAs-based grating spectrometer through a
multimode fiber.
For the nonlinear spectroscopy measurement, a Ti-Sapphire laser oscillator
(Coherent Chameleon) was coupled to an OPO (optical parametric oscillator, Coherent
Mira) to provide a pump beam with a wavelength tunable from 1 μm to 1.6 μm (pulse
duration ~250fs, repetition rate of 80 MHz). The laser was focused on the metasurface
using a 0.14 NA objective with a beam size of ~225 um2. The laser power was adjusted
using the combination of a half waveplate and a linear polarizer. The transmitted
fundamental and third harmonic waves were then collected by a high numerical aperture
objective (Nikon Plan Apo Lambda, 60x, 0.95 NA), such that any diffracted THG was
collected. The THG spectra from either the metasurface or an un-patterned Si film were
then acquired using a grating spectrometer (Horiba iHR320). A short-pass filter
106
(Semrock, 790 nm blocking edge BrightLine®
) was placed in front of the spectrometer to
filter out the IR pump beam.
Figure D.1. Schematic of the linear/nonlinear spectroscopic measurement set-up for the
investigation of the metasurface.
D.1.2 Absolute THG Efficiency-Measurement from OPO
For the absolute THG efficiency measurement using the OPO, we first applied a
large pump intensity (3.2 GW cm-2
) on the metasurface, such that the THG signal (~50
nW) could be directly read from a silicon photodetector (Newport 818 series). The
absolute THG power from the metasurface was estimated with an additional correction
coefficient considering the transmittance of the 0.95 NA objective (84%) and the short-
pass filter (95%).
This high power measurement was then used as a reference to calibrate a photo-
multiplier tube (PMT) that was used for THG power measurements under relatively low
pump intensity. The PMT was connected to a lock-in amplifier and a chopper for better
signal-to-noise ratio.
107
Figure D.2. Schematic of the absolute THG efficiency measurement set-up with OPO.
D.1.3 Absolute THG Efficiency-Measurement from OPA
The laser source for the 1 kHz THG measurements is based on a Ti:Sapphire
oscillator (Micra, Coherent) with its output seeded a Ti:Sapphire Coherent Legend (USP-
HE) amplifier, operating at 1 kHz repetition rate. The Legend amplifier provides pulses
centered at 800 nm, with 40 fs duration and 2.2 mJ energy per pulse. The output of the
Legend amplifier was used to generate tunable pulses (250-2500 nm) in an optical
parametric amplifier (TOPAS, Coherent). To align the laser wavelength with the Fano
resonance of the metasurface, the TOPAS output signal was tuned to be centered at 1350
nm. Using a 0.14 NA microscope objective, the 1350 nm pump was focused on the
sample to ~20 m spot size. After the sample, the THG was collected in the forward
direction using a second objective microscope (Nikon Plan Apo Lambda, 60x, 0.95 NA)
and focused onto the slit entrance of a spectrometer (Shamrock 303i, Andor) coupled
with an EM-CCD (Newton, Andor). A short-pass filter (cut-off at 790 nm) was used to
reject pump photons before detection. In order to control the pump fluence, a half wave-
plate placed before the polarizer was used. For each pump power, THG signal was
108
collected for 25 seconds. In order to convert THG intensity into energy and overcome
loses in the detection system; the power equivalence of each CCD count was determined
by measuring the power of a laser beam before sending it to the detector.
Figure D.3. Schematic of the absolute THG efficiency measurement set-up with OPA.
D.2 Device Performance versus Incident Angle
The simulated angle-dependent linear transmittance of the metasurface for both s-
and p- polarized light is presented in Fig. D.4. The range of incident angles (0° to 8°) was
chosen to match the numerical aperture of the objective lens on the illumination side.
It can be observed that the spectral response of the metasurface is strongly
dependent on the incident angle and the dependence is drastically different for s- and p-
polarized incident light. For s-polarized light, the excitation of the “bright” electric dipole
resonance is unaltered as the incident electric field is parallel to the metasurface layer.
However, the out-of-plane incident magnetic field leads to stronger coupling from free-
space to the “dark” magnetic dipole leading to an increased radiative loss and reduced Q-
factor. For p-polarized light, the incident electric field is gradually rotated out-of-plane,
resulting in a frequency mismatch between the electric and magnetic dipole resonance
leading to gradual damping of the Fano resonance.
109
Figure D.4. Simulated Linear transmittance of the metasurface as a function of incident
angle for (a) s- and (b) p-polarized light.
110
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